Xiaoquan Tang, Long Zhang, Xiuting Li,
Bayesian augmented Lagrangian algorithm for system identification,
Systems & Control Letters,
Volume 120,
2018,
Pages 9-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.011.
(http://www.sciencedirect.com/science/article/pii/S016769111830135X)
Abstract: Nonlinear Auto-Regressive model with eXogenous input (NARX) is one of the most popular black-box model classes that can describe many nonlinear systems. The structure determination is the most challenging and important part during the system identification. NARX can be formulated as a linear-in-the-parameters model, then the identification problem can be solved to obtain a sparse solution from the viewpoint of the weighted l1 minimization problem. Such an optimization problem not only minimizes the sum squares of model errors but also the sum of reweighted model parameters. In this paper, a novel algorithm named Bayesian Augmented Lagrangian Algorithm (BAL) is proposed to solve the weighted l1 minimization problem, which is able to obtain a sparse solution and enjoys fast computation. This is achieved by converting the original optimization problem into distributed suboptimization problems solved separately and penalizing the overall complex model to avoid overfitting under the Bayesian framework. The regularization parameter is also iteratively updated to obtain a satisfied solution. In particular, a solver with guaranteed convergence is constructed and the corresponding theoretical proof is given. Two numerical examples have been used to demonstrate the effectiveness of the proposed method in comparison to several popular methods.
Keywords: System identification; Weighted l1 minimization; Augmented Lagrangian; Bayesian; NARX

Tao Bian, Zhong-Ping Jiang,
Stochastic and adaptive optimal control of uncertain interconnected systems: A data-driven approach,
Systems & Control Letters,
Volume 115,
2018,
Pages 48-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118300434)
Abstract: This paper provides a novel non-model-based, data-driven stochastic H∞ control design for linear continuous-time stochastic interconnected systems with unknown dynamics. Our contributions are three-fold. First, we develop a tool to show how to assign an arbitrarily small input-to-output stochastic L2 gain of the closed-loop system, by combining the gain assignment technique with the zero-sum dynamic game-based H∞ control design. Second, robustness to dynamic uncertainties is tackled using the small-gain theory. Third, we develop a non-model-based stochastic robust adaptive dynamic programming (RADP) algorithm for adaptive optimal controller design. In sharp contrast to the existing methods, the obtained algorithm is based on value iteration (VI), and the knowledge of an initial stabilizing control policy is no longer needed. An example of a power electronic system is adopted to illustrate the obtained results.
Keywords: Robust adaptive dynamic programming (RADP); 
               H∞ control; Stochastic system; Zero-sum differential game; Value iteration; Small-gain

Fei Ye, Bo Sun, Linlin Ou, Weidong Zhang,
Disturbance observer-based control for consensus tracking of multi-agent systems with input delays from a frequency domain perspective,
Systems & Control Letters,
Volume 114,
2018,
Pages 66-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117302244)
Abstract: The consensus tracking controller design of multi-agent systems with diverse input delays is studied in this paper. A universal block diagram is established to describe the linear multi-agent systems based on transfer functions. The stabilization of the whole system is decomposed into the zero steady-state error control problem of each independent agent. A sufficient and necessary condition is accordingly deduced to impose on each controller. Based on the H2 performance index of each subsystem, both the optimal consensus controller and disturbance observer (DOB) are derived analytically. The distributed H2 DOB-based consensus controller can not only achieve consensus tracking for the reference input, but also reject the effects of external disturbance and model uncertainty. Some simulations are performed to illustrate the validity of the proposed design approach.
Keywords: Multi-agent systems; Disturbance observer; Input delay; 
               H2 performance index; Frequency domain

Pavel Pakshin, Julia Emelianova, Mikhail Emelianov, Krzysztof Galkowski, Eric Rogers,
Passivity based stabilization of repetitive processes and iterative learning control design,
Systems & Control Letters,
Volume 122,
2018,
Pages 101-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118301646)
Abstract: Repetitive processes are a class of 2D systems that arise in the modeling of physical systems and also as a setting for iterative learning control design. For linear dynamics experimental validation of iterative learning control laws designed in this setting has been successfully achieved. Examples also exist where a linear model is not sufficient for analysis and control law design. This has led to research on the development of a stability and control law design theory for nonlinear repetitive processes. In this paper new results on a passivity based approach to control law design for these processes are developed. These results are then extended to iterative learning control, resulting in a design where tuning of the control law to achieve better performance is possible.
Keywords: Repetitive processes; Passivity; Stability; Iterative learning control design

Gen Qi Xu,
Necessary condition of linear distributed parameter systems with exact controllability,
Systems & Control Letters,
Volume 118,
2018,
Pages 109-115,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118301129)
Abstract: In this paper, we studied the necessary condition of distributed parameter system with exact controllability. Let Φ0t be the control mapping. We introduce new a class of control operators that is called the I-class control which satisfy R(Φ0t)∩R(T(t)) is closed set for t>0. If the system is exactly controllable in finite time τ, then the semigroup T(t) must have closed range. In particular, if the generator of T(t) has compact resolvent, its spectra distribute in a strip parallel to imaginary axis. As an application we assert that the systems associated with the immediately norm-continuous semigroups are never exact controllable for zero-class or I-class controls.
Keywords: Linear system; Exact controllability; Necessary condition; Immediately norm-continuous semigroup

Quan Quan, Kai-Yuan Cai,
Saturated repetitive control for a class of nonlinear systems: A contraction mapping method,
Systems & Control Letters,
Volume 122,
2018,
Pages 93-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118301889)
Abstract: Contraction mapping methods do not need to know about the concrete form of plant models like the Lyapunov method. This is the biggest advantage over other methods in the field of iterative learning control for example. However, it is difficult to use such a tool to analyze repetitive control systems. This paper proposes a contraction mapping method based on spectral theory to design a saturated repetitive controller for a class of nonlinear systems, where the derived necessary and sufficient condition on the spectral radius can reduce the conservatism as much as possible. The feasibility of our work is demonstrated through a robotic manipulator tracking example.
Keywords: Repetitive control; Nonlinear systems; Contraction mapping; Spectral theory; Saturation

Yongzhao Hua, Xiwang Dong, Liang Han, Qingdong Li, Zhang Ren,
Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input,
Systems & Control Letters,
Volume 122,
2018,
Pages 67-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118301804)
Abstract: This paper investigates the formation-containment tracking problems for general linear multi-agent systems with a tracking-leader of unknown control input, where the agents are classified into a tracking-leader, several formation-leaders and followers. The formation-leaders are required to accomplish a given time-varying formation configuration and track the desired trajectory generated by the tracking-leader simultaneously, while the followers need to converge to the convex hull spanned by the formation-leaders. Firstly, based on the neighboring relative information, a formation-containment tracking protocol is proposed under the influences of the tracking-leader’s unknown input. Then an algorithm is given to determine the control parameters, where a general formation-containment tracking feasible constraint is presented. It is proved that the given formation-containment tracking can be achieved under the discontinuous protocol. Furthermore, in order to avoid the large chattering of the control inputs, a continuous formation-containment tracking protocol is also presented, under which the errors can converge to an arbitrarily small neighborhood of zero. Finally, a simulation example is given to verify the theoretical results.
Keywords: Formation control; Containment control; Distributed tracking; Multi-agent systems

Alexander Domoshnitsky, Roman Shklyar,
Positivity for non-Metzler systems and its applications to stability of time-varying delay systems,
Systems & Control Letters,
Volume 118,
2018,
Pages 44-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.009.
(http://www.sciencedirect.com/science/article/pii/S016769111830094X)
Abstract: In 1950, Wazewski obtained the following necessary and sufficient condition for positivity of linear systems of ordinary differential equations: the matrix of coefficients is Metzler (i.e. off-diagonal elements in the matrix of coefficients are nonnegative). No results on the positivity of solutions to delay systems in the case where the matrix is non-Metzler were expected to be obtained. It was demonstrated that for delay systems the Wazewski condition is not a necessary one. We prove results on positivity of solutions for non-Metzler systems of delay differential equations. New explicit tests for exponential stability are obtained as applications of results on positivity for non-Metzler systems. Examples demonstrate possible applications of our theorems to stabilization. For instance, in view of our results, the implicit requirement on dominance of the main diagonal can be skipped. Our approach is based on nonoscillation of solutions and positivity of the Cauchy functions of scalar diagonal delay differential equations.
Keywords: Time-delay systems; Positive systems; Exponential stability; Nonoscillation; Cauchy matrix

Aldo-Jonathan Muñoz-Vázquez, Vicente Parra-Vega, Anand Sánchez-Orta, Gerardo Romero-Galván,
Quadratic Lyapunov functions for stability analysis in fractional-order systems with not necessarily differentiable solutions,
Systems & Control Letters,
Volume 116,
2018,
Pages 15-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118300719)
Abstract: Solutions of fractional-order differintegral equations are generally not necessarily integer-order differentiable, neither in the strong nor in the weak sense, thus limiting the stability analysis in systems based on the most conventional fractional-order operators. In this paper, a consistent and well-posed definition for fractional-order systems is performed based on the study of alternative fractional-order operators that preserve the most interesting and useful properties of differintegrals, even in the case of not necessarily integer-order (weakly) differentiable functions. In addition, it is shown that these operators comply to a recently verified well-known inequality, which allows us to demonstrate Mittag-Leffler stability in a more general class of fractional-order systems, considering quadratic Lyapunov functions, by demonstrating a generalization of the Lyapunov direct method for a class of fractional-order nonlinear systems. Illustrative examples are given to highlight the feasibility of the proposed method, and a multivariable fractional integral sliding mode control application is presented.
Keywords: Fractional-order systems; Mittag-Leffler stability; Lyapunov direct method; Nonlinear systems

Ioannis Exarchos, Evangelos A. Theodorou, Panagiotis Tsiotras,
Stochastic L1-optimal control via forward and backward sampling,
Systems & Control Letters,
Volume 118,
2018,
Pages 101-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118301130)
Abstract: The aim of this work is to present a sampling-based algorithm designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). Specifically, we address the class of problems in which the running cost of the performance index involves an L1-type minimization problem in terms of the control effort. Such problems are typically called minimum fuel problems in optimal control literature. By means of a nonlinear version of the Feynman–Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton–Jacobi–Bellman equation, expressed in the form of a system of decoupled FBSDEs. This system of FBSDEs can be solved by employing linear regression techniques.
Keywords: Stochastic L1 optimal control; Forward and backward stochastic differential equations

Fudong Ge, Thomas Meurer, YangQuan Chen,
Mittag-Leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters,
Systems & Control Letters,
Volume 122,
2018,
Pages 86-92,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118301890)
Abstract: The purpose of this paper is to investigate the observer-based boundary output feedback control for subdiffusion processes governed by coupled semilinear time fractional diffusion systems (TFDSs) with spatially varying parameters. For this, backstepping technique is used to Mittag-Leffler stabilize the coupled semilinear observer error dynamic systems. We then design an observer-based output feedback controller at the right boundary to realize the Mittag-Leffler stability of the closed-loop systems at hand. A numerical example is finally included to test our methods.
Keywords: Backstepping observers; Boundary feedback control; Coupled semilinear time fractional diffusion systems; Mittag-Leffler stability

Amir Ali Ahmadi, Bachir El Khadir,
A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function,
Systems & Control Letters,
Volume 121,
2018,
Pages 50-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.013.
(http://www.sciencedirect.com/science/article/pii/S0167691118301373)
Abstract: We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.
Keywords: Polynomial vector fields; Algorithms for testing asymptotic stability; Polynomial Lyapunov functions; Sum of squares optimization; Nonlinear dynamics

A. Anderson, A.H. González, A. Ferramosca, A. D’Jorge, E. Kofman,
Robust MPC suitable for closed-loop re-identification, based on probabilistic invariant sets,
Systems & Control Letters,
Volume 118,
2018,
Pages 84-93,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118301099)
Abstract: This work extends a recent set-based Model Predictive Control (MPC) scheme for closed loop re-identification that solves the potential conflict between the simultaneous persistent excitation of the system and the stabilization of the closed-loop system. Based on the original scheme proposed in González et al. (2014), this manuscript extends those results by taking into account model uncertainties and by exploiting the knowledge of the probability distribution of the excitation signal used to identify the plant. The robust extension solves the main drawback of the previous work, which was limited to a nominal analysis while the need of re-identificationassumes the presence of model uncertainties. In addition, the probabilistic analysis allows the use of smaller target sets computed as Probabilistic Invariant Sets (PIS), improving the system performance during the identification procedure. Simulation results show the practical benefits of the novel robust strategy.
Keywords: Model predictive control; Closed-loop re-identification; Probabilistic invariant sets

Patrizio Tomei, Cristiano Maria Verrelli,
Advances on adaptive learning control: The case of non-minimum phase linear systems,
Systems & Control Letters,
Volume 115,
2018,
Pages 55-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118300562)
Abstract: The adaptive learning control theory is extended to include the case of non-minimum phase (time-invariant) linear systems with uncertain parameters. The existence of two approximate solutions to the related output tracking problem is proved. Exponential tracking of periodic output reference signals is guaranteed, along with the exponential estimation of the constant system parameters and of the constant coefficients characterizing the truncated Fourier series expansion for the periodic input reference signal.
Keywords: Adaptive learning; Linear uncertain systems; Adaptive observers; Non-minimum phase

Yuecheng Yang, Dimos V. Dimarogonas, Xiaoming Hu,
Opinion consensus under external influences,
Systems & Control Letters,
Volume 119,
2018,
Pages 23-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118301014)
Abstract: As a means to regulate the continuous-time bounded confidence opinion dynamics, an exo-system to the original Hegselmann–Krause model is added. Some analysis is made about the properties of the combined system. Two theorems are provided in this article in terms of sufficient conditions of the exo-system that can guarantee opinion consensus for any initial conditions. Two more corollaries are given to describe the resulting synchronized opinions.
Keywords: Opinion dynamics; Multi-agent system

Mattia Mattioni, Salvatore Monaco, Dorothée Normand-Cyrot,
Nonlinear discrete-time systems with delayed control: A reduction,
Systems & Control Letters,
Volume 114,
2018,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300288)
Abstract: In this work, the notion of reduction is introduced for discrete-time nonlinear input-delayed systems. The retarded dynamics is reduced to a new system which is free of delays and equivalent (in terms of stabilizability) to the original one. Different stabilizing strategies are proposed over the reduced model. Connections with existing predictor-based methods are discussed. The methodology is also worked out over particular classes of time-delay systems as sampled-data dynamics affected by an entire input delay.
Keywords: Discrete-time systems; Nonlinear systems; Time-delay systems

V. Barbu, L. Tubaro,
Exact controllability of stochastic differential equations with multiplicative noise,
Systems & Control Letters,
Volume 122,
2018,
Pages 19-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118301774)
Abstract: One proves that the n-D stochastic controlled equation dX(t)+A(t)X(t)dt=σ(X(t))dW(t)+B(t)u(t)dt, where σ∈Lip(Rn,ℒ(Rd,Rn)), A(t)∈ℒ(Rn) and B(t)∈ℒ(Rn,Rn) is invertible, is exactly controllable with high probability in each y∈Rn such that σ(y)=0 on each finite interval (0,T). An application to approximate controllability of the stochastic heat equation is given. The case where B∈ℒ(Rm,Rn), 1≤m<n and the pair (A,B) satisfies the Kalman rank condition is also studied.
Keywords: Stochastic equation; Controllability; Feedback controller

Mingxuan Shen, Weiyin Fei, Xuerong Mao, Yong Liang,
Stability of highly nonlinear neutral stochastic differential delay equations,
Systems & Control Letters,
Volume 115,
2018,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.013.
(http://www.sciencedirect.com/science/article/pii/S0167691118300422)
Abstract: Stability criteria for neutral stochastic differential delay equations (NSDDEs) have been studied intensively for the past several decades. Most of these criteria can only be applied to NSDDEs where their coefficients are either linear or nonlinear but bounded by linear functions. This paper is concerned with the stability of hybrid NSDDEs without the linear growth condition, to which we will refer as highly nonlinear ones. The stability criteria established in this paper will be dependent on delays.
Keywords: Neutral stochastic differential delay equation; Nonlinear growth condition; Asymptotic stability; Delay dependent; Markovian switching

Xu Ma, Nicola Elia,
A distributed continuous-time method for non-convex QCQPs,
Systems & Control Letters,
Volume 121,
2018,
Pages 16-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118301634)
Abstract: This paper studies non-convex Quadratically Constrained Quadratic Programmings (QCQPs) via the continuous-time optimization dynamics. We first develop an easily checkable necessary and sufficient condition that characterizes whether a KKT point will also be a saddle-point (the pair of primal and dual optima) for a non-convex QCQP. Then we analyze the semistability of the saddle-point equilibrium set with respect to the proposed optimization dynamics. We also point out that, for certain networked QCQPs, the proposed approach exhibits an intrinsic distributed computational structure.
Keywords: QCQP; Primal–dual optimization dynamics; Saddle-point; Distributed computational structure

Erik Weitenberg, Claudio De Persis,
Robustness to noise of distributed averaging integral controllers in power networks,
Systems & Control Letters,
Volume 119,
2018,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118301117)
Abstract: We investigate the robustness of distributed averaging integral controllers for optimal frequency regulation of power networks to noise in measurements, communication and actuation. Specifically, using Lyapunov techniques, we show a property related to input-to-state stability of the closed loop system with respect to this noise. Using this result, a tuning trade-off between controller performance and noise rejection is highlighted.
Keywords: Lyapunov methods; Networked systems; Power networks; Robustness analysis; Cyber–physical systems

Arash Sadeghzadeh,
On exploiting inexact scheduling parameters for gain-scheduled control of linear parameter-varying discrete-time systems,
Systems & Control Letters,
Volume 117,
2018,
Pages 1-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.012.
(http://www.sciencedirect.com/science/article/pii/S016769111830077X)
Abstract: This paper is concerned with the problem of gain-scheduled controller design for parameter-varying discrete-time systems. In practice, the scheduling parameters are only available with limited accuracy due to the measurement errors. In the present paper, these uncertainties are systematically taken into account for the gain-scheduled controller synthesis to achieve improved performance in practical situations. It is assumed that all the matrices of the state-space model of the plant have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameters. The merit of the proposed method is its capability in dealing with the measurement error less conservatively than available approaches while it can also encompass the traditional methods employing the exact scheduling parameters in a less conservative manner. A comprehensive numerical example demonstrates the effectiveness of the proposed method.
Keywords: Gain-scheduled controller; Discrete-time system; Parameter-varying system; Bounded variation rate; Inexact scheduling parameters; Induced l2-gain performance

Tanagorn Jennawasin, David Banjerdpongchai,
Design of state-feedback control for polynomial systems with quadratic performance criterion and control input constraints,
Systems & Control Letters,
Volume 117,
2018,
Pages 53-59,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118300823)
Abstract: This paper presents a novel convex optimization approach to design state-feedback control for polynomial systems. Design criteria are comprised of a quadratic cost function and bounded magnitudes of control inputs. Specifically, we formulate a control synthesis of closed-loop systems operated in a given bounded domain characterized by a semi-algebraic set. We consider an extended class of rational Lyapunov functions and derive an upper bound of the cost function, together with a state-feedback control law. By exploiting bounds on the control input magnitudes, the controller design condition can be cast as a parameter-dependent linear matrix inequality (PDLMI), which is convex optimization and can be efficiently solved by sum-of-squares (SOS) technique. In addition, we derive a sufficient condition to compute a lower bound of the cost function. When choosing polynomial structure of the solution candidate, the lower bound can also be written as PDLMI. Numerical examples are provided to illustrate the effectiveness of the proposed design.
Keywords: Convex optimization; Polynomial systems; Quadratic performance criterion; Control input constraint; Rational Lyapunov functions; State-feedback control

Peng Yi, Jinlong Lei, Yiguang Hong,
Distributed resource allocation over random networks based on stochastic approximation,
Systems & Control Letters,
Volume 114,
2018,
Pages 44-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118300306)
Abstract: In this paper, we study a resource allocation problem in which a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint and allocation feasibility constraints, where the global objective function is the sum of agents’ local objective functions. Each agent can only get noisy observations of its local gradient function and its local resource, which cannot be shared by other agents or transmitted to a center. There also exist communication uncertainties such as time-varying topologies (described by random graphs) and additive channel noises. To solve the resource allocation with uncertainties, we propose a stochastic approximation based distributed algorithm, and prove that agents can collaboratively achieve the optimal allocation with probability one by virtue of the ordinary differential equation (ODE) method for stochastic approximation. Finally, simulations related to the demand response management in power systems verify the effectiveness of the proposed algorithm.
Keywords: Distributed optimization; Resource allocation; Stochastic approximation; Random graph; Demand response

Carsten W. Scherer, Joost Veenman,
Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions,
Systems & Control Letters,
Volume 121,
2018,
Pages 7-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.08.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118301518)
Abstract: This paper provides a complete link between dissipative systems theory and a celebrated result on stability analysis with integral quadratic constraints (IQCs). This is achieved with a new stability characterization for feedback interconnections based on the notion of finite-horizon integral quadratic constraints with a terminal cost. As the main benefit, this opens up opportunities for guaranteeing constraints on the transient responses of trajectories in feedback loops within absolute stability theory. For systems affected by parametric uncertainties, we show how to generate tight robustly invariant ellipsoids on the basis of a classical frequency-domain stability test, with illustrations by a numerical example.
Keywords: Dissipative systems theory; Integral quadratic constraints; Absolute stability theory; Linear matrix inequalities

Damián Marelli, Mohsen Zamani, Minyue Fu, Brett Ninness,
Distributed Kalman filter in a network of linear systems,
Systems & Control Letters,
Volume 116,
2018,
Pages 71-77,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300707)
Abstract: This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in the state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed method provides, at each node, an estimation of the state parameter, only based on locally available measurements and those from the neighbor nodes. The special feature of this method is that it exploits the particular structure of the considered network to obtain an estimate using only one prediction/update step at each time step. We show that the estimate produced by the proposed method asymptotically approaches that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.
Keywords: Estimation; Kalman filter; Distributed systems

Xinzhi Liu, Kexue Zhang,
Stabilization of nonlinear time-delay systems: Distributed-delay dependent impulsive control,
Systems & Control Letters,
Volume 120,
2018,
Pages 17-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118301361)
Abstract: This technical note studies impulsive stabilization of general nonlinear systems with time-delay. Distributed time-delay is considered in the proposed nonlinear impulsive controller. Using Lyapunov–Razumikhin method, an exponential stability criterion is constructed, which is then applied to investigate stabilization of a linear time-delay system under linear distributed-delay dependent impulsive control. Sufficient conditions on the system parameters, impulsive control gains, impulsive instants and distributed delays are obtained in the form of an inequality for global exponential stability. In these results, it is shown that an unstable time-delay system can be successfully stabilized by distributed-delay dependent impulses. It is worth noting that the proposed impulsive controllers are independent of the system states at each impulsive instant, and the states with distributed delays play the key role in the stabilization process. A numerical example is provided to demonstrate the efficiency of the main results.
Keywords: Impulsive control; Distributed delay; Exponential stability; Lyapunov–Razumikhin method

Maxim Staritsyn,
On “discontinuous” continuity equation and impulsive ensemble control,
Systems & Control Letters,
Volume 118,
2018,
Pages 77-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118301087)
Abstract: The note is devoted to a class of singular ensemble control problems: we consider the continuity equation driven by a control-affine vector field subject to the constraint on the L1-norm of the input function. Since no geometric constraints on control are imposed, solutions to the continuity equation can, potentially, tend somehow to discontinuous measure-valued functions. We elaborate a representation of such discontinuous, generalized solutions through an ordinary control equation being a time reparameterization of the characteristic ordinary differential equation (ODE) of the original continuity equation. By virtue of standard results from impulsive control theory of ODEs, we perform a constructive formula for generalized solutions in terms of a measure differential equation. Finally, we state an optimal impulsive control problem for the singular continuity equation, and prove the existence of its solution. The obtained results can be useful for modeling and analysis of impulsive control problems with uncertain initial data.
Keywords: Continuity equation; Ensemble control; Impulsive control; Optimal control; Generalized solutions of control problems

Dong Zhao, Steven X. Ding, Youqing Wang, Yueyang Li,
Krein-space based robust H∞ fault estimation for two-dimensional uncertain linear discrete time-varying systems,
Systems & Control Letters,
Volume 115,
2018,
Pages 41-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300550)
Abstract: In this study, the robust H∞ fault estimation problem for two-dimensional linear time-varying systems with norm-bounded unknown input, measurement noise, and time-varying process uncertainty is investigated. By introducing an equivalent auxiliary system and a new certain indefinite quadratic form performance function, the system uncertainty can be appropriately considered into the new performance function and the fault estimator design is converted to the minimization problem of a quadratic form. Based on the partially equivalence property between the deterministic quadratic form problem and the Krein space estimation theory, the two-dimensional H∞ fault estimation problem can be solved via signal deconvolution in Krein space. Through employing projection operation and Riccati-like difference equation in two dimensions, both the recursive form fault estimator and the explicit condition for existence of the estimator are derived. One Darboux equation example is provided to illustrate the effectiveness of the proposed fault estimator.
Keywords: Two-dimensional systems; Fault estimation; Krein space; Uncertain systems; Time-varying systems

Dan Pilbauer, Wim Michiels, Jaroslav Bušek, David Osta, Tomáš Vyhlídal,
Control design and experimental validation for flexible multi-body systems pre-compensated by inverse shapers,
Systems & Control Letters,
Volume 113,
2018,
Pages 93-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118300033)
Abstract: A complex methodology for control of flexible multi-body systems is proposed with the objective to achieve a favorable distribution of system motion so that the oscillatory mode of the flexible part is not excited. As the key element, the recently proposed concept of a feedback loop with an inverse distributed delay shaper is adopted. Unlike in existing works, the mutual coupling between the primary (controlled) structure and secondary (flexible) structure of oscillatory nature is explicitly taken into account in the controller design. First, an easy to apply method to isolate the flexible mode to be targeted in the shaper design is proposed. Secondly, the interconnection of the system, shaper and the controller is formulated as a set of delay differential algebraic equations. Then the spectral optimization control design technique is applied to achieve fast dynamics of the infinite dimensional system. The viability of the overall methodology is validated by both simulations and experiments in an extensive case study example.
Keywords: Time-delay; Inverse shapers; Vibration control; Spectral optimization; Spectral abscissa

Víctor Ayala, Adriano Da Silva, Max Ferreira,
Affine and bilinear systems on Lie groups,
Systems & Control Letters,
Volume 117,
2018,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118300793)
Abstract: In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affine systems on compact and solvable Lie groups. We also show that the controllability property of bilinear systems is very restricted and may only be achieved if the state space G is an Euclidean space.
Keywords: Affine systems; Bilinear systems; Controllability

Hsueh-Ju Chen, Alexander Lanzon,
Closed-loop stability analysis of discrete-time negative imaginary systems,
Systems & Control Letters,
Volume 114,
2018,
Pages 52-58,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118300276)
Abstract: We derive necessary and sufficient conditions for stability analysis of a positive feedback interconnection of a discrete-time negative imaginary system and a discrete-time strictly negative imaginary system. General stability analysis results for continuous-time negative imaginary systems connected in positive feedback have recently been proposed. Those recent results extend previous theorems by removing restrictive assumptions on the infinite frequency gains imposed in the earlier literature and by extending the class of negative imaginary systems for which the results are applicable to include systems with free body dynamics (i.e., poles at the origin). Here, we present the discrete-time counterparts of the aforementioned recently developed results which specialise to simple and easy-to-check conditions under specific assumptions. Last, we illustrate some of the results by several examples.
Keywords: Discrete-time; Negative imaginary systems; Feedback stability; Robust control

Evgenij Barabanov, Adam Czornik, Michał Niezabitowski, Aliaksei Vaidzelevich,
Influence of parametric perturbations on Lyapunov exponents of discrete linear time-varying systems,
Systems & Control Letters,
Volume 122,
2018,
Pages 54-59,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118301762)
Abstract: In this paper we investigate the problem of influence of parametric perturbations on the Lyapunov spectrum of the discrete linear time-varying system. The main result of the paper is that for any two sequences of positive real numbers and any rate of convergence there exist a discrete linear time-varying system and a perturbation tending to zero with the given rate of convergence such that the spectra of the perturbed and unperturbed systems coincide with the a priori given sequences. Moreover, we show that this phenomenon is possible even when the perturbations are different from zero, rarely, in a certain sense. Finally, as a conclusion from the main result, we obtain that the separation type and the index of exponential stability may vary arbitrarily under the influence of exponentially decreasing perturbations.
Keywords: Lyapunov exponents; Discrete linear time-varying systems; Coefficient perturbations; Separation type; Stability index

A.A. Malikopoulos, C.D. Charalambous, I. Tzortzis,
The average cost of Markov chains subject to total variation distance uncertainty,
Systems & Control Letters,
Volume 120,
2018,
Pages 29-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.08.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118301488)
Abstract: This paper addresses the problem of controlling a Markov chain so as to minimize the long-run expected average cost per unit time when the invariant distribution is unknown but we know it belongs to a given uncertain set. The mathematical model used to describe this set is the total variation distance uncertainty. We show that the equilibrium control policy, which yields higher probability to the states with low cost and lower probability to the states with the high cost, is an optimal control policy that minimizes the average cost. Recognition of such a policy may be of value in practical situations with constraints consistent to those studied here when the invariant distribution is uncertain and deriving online an optimal control policy is required.
Keywords: Stochastic optimal control; Controlled Markov chain; Average cost; Total variation distance

Aladin Crnkić, Vladimir Jaćimović,
Swarms on the 3-sphere with adaptive synapses: Hebbian and anti-Hebbian learning rule,
Systems & Control Letters,
Volume 122,
2018,
Pages 32-38,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118301786)
Abstract: We introduce and analyze several models of swarm dynamics on the sphere S3 with adaptive (state-dependent) interactions between agents. The equations describing the interaction dynamics are variations of the classical Hebbian principle from Neuroscience. We study asymptotic behavior in models with various realizations of Hebbian and anti-Hebbian learning rules. The swarm with the Hebbian rule and strictly nonnegative (attractive) interactions evolves towards consensus. If the Hebbian rule allows both attractive and repulsive interactions the swarm converges to bipolar configuration. The most interesting is the model with anti-Hebbian learning rule with both attractive and repulsive interactions. This model displays a rich variety of dynamical regimes and stationary formations, depending on the number of agents and system parameters. We prove that the model with such anti-Hebbian rule evolves towards a stable stationary configuration if the system parameter is above a certain bifurcation threshold. Finally, some simulation results are presented demonstrating how these theoretical results can be applied to coordination of rotating bodies in 3D space; this is done by mapping the trajectories from S3 to special orthogonal group SO(3).
Keywords: Multi-agent system; 3-sphere; Coordination; Consensus; Adaptive synapses

Qian Feng, Sing Kiong Nguang,
Dissipative delay range analysis of coupled differential–difference delay systems with distributed delays,
Systems & Control Letters,
Volume 116,
2018,
Pages 56-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118300732)
Abstract: This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential–difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains many models of linear delay systems as special cases. A novel Lyapunov–Krasovskii functional with non-constant matrix parameters, which are related to the delay value polynomially, is applied to derive stability conditions. By constructing this new functional, sufficient conditions in terms of robust linear matrix inequalities (LMIs) can be derived, which guarantee range stability of a linear CDDS subject to dissipative constraints. To solve the resulting robust LMIs numerically, we apply the technique of sum of squares programming together with matrix relaxations without introducing any potential conservatism to the original robust LMIs. Furthermore, the proposed methods can be extended to solve delay margin estimation problems for a linear CDDS subject to prescribed dissipative constraints. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.
Keywords: Coupled differential–difference systems; Range stability; Dissipativity; Sum of square programming

Junmin Peng, Chaoyong Li, Xudong Ye,
Cooperative control of high-order nonlinear systems with unknown control directions,
Systems & Control Letters,
Volume 113,
2018,
Pages 101-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.014.
(http://www.sciencedirect.com/science/article/pii/S0167691118300215)
Abstract: In this paper, we investigate output synchronization problem of nonlinear systems that can be transformed into strict feedback form with unknown control direction. To this end, an augmented Laplacian potential function is introduced to construct local level distributed adaptive controllers such that outputs of networked agents can be synchronized while all other states maintain bounded. Moreover, tuning functions are designed to reduce the order of the parameter updater. In contrast to conventional adaptive backstepping procedure, both the parameter updating law and tuning function of the proposed scheme take advantage of information flow among networked agents and thus distributive in nature. It is proved that output synchronization of the entire network can be achieved by properly choosing Nussbaum functions, provided the information graph is undirected and connected. Furthermore, we also proposed a way to define a proper Nussbaum function. Simulation results are presented to verify the effectiveness of the proposed schemes.
Keywords: Synchronization; Nussbaum; Adaptive control; Strict feedback

Fu Lin, Jie Chen,
Learning low-complexity autoregressive models via proximal alternating minimization,
Systems & Control Letters,
Volume 122,
2018,
Pages 48-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118301701)
Abstract: We consider the estimation of the state transition matrix in vector autoregressive models, when time sequence data is limited but nonsequence steady-state data is abundant. To leverage both sources of data, we formulate the least squares minimization problem regularized by a Lyapunov penalty. We impose cardinality or rank constraints to reduce the complexity of the autoregressive model. The resulting nonconvex, nonsmooth problem is solved by using the proximal alternating linearization method (PALM). We prove that PALM is globally convergent to a critical point and that the estimation error monotonically decreases. Explicit formulas are obtained for the proximal operators to facilitate the implementation of PALM. We demonstrate the effectiveness of the developed method by numerical experiments.
Keywords: Autoregressive models; Lyapunov penalty; Nonconvex nonsmooth problem; Steady-state data; Proximal alternating linearized minimization

Jing Chen, Feng Ding, Yanjun Liu, Quanmin Zhu,
Multi-step-length gradient iterative algorithm for equation-error type models,
Systems & Control Letters,
Volume 115,
2018,
Pages 15-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300458)
Abstract: This letter develops a multi-step-length gradient iterative algorithm for equation-error type (EET) models. The algorithm analysis is based upon the gradient search principle. By applying the Gram–Schmidt procedure, the EET model can be turned into an orthogonal model, in which each parameter in the parameter vector is independent of the other parameters. Then a multi-step-length gradient iterative algorithm is proposed for the orthogonal model, and can estimate the parameters in one iteration. Finally, based on the estimated parameters, the parameter estimates of the EET model can be computed. Different from the traditional gradient iterative algorithm which has slower convergence rates and is sensitive to the initial values of the unknown variables, the method in this letter has quicker convergence rates and is robust to the initial values of the unknown variables. The simulation studies demonstrate the feasibility and effectiveness of the proposed algorithm.
Keywords: Parameter estimation; Gradient algorithm; Multi-step-length; Convergence rate; EET model

Shiguo Peng, Feiqi Deng, Yun Zhang,
A unified Razumikhin-type criterion on input-to-state stability of time-varying impulsive delayed systems,
Systems & Control Letters,
Volume 116,
2018,
Pages 20-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118300616)
Abstract: This paper discusses the problem of input-to-state stability (ISS) of time-varying impulsive delayed systems. By introducing a switching parameter and using the notion of average impulsive interval, a unified Razumikhin-type criterion on ISS which is simultaneously effective for stabilizing impulses and destabilizing impulses is derived. The condition which requires the coefficient of the estimated upper bound of the derivative of a Lyapunov function to be constant in the existing results on ISS of impulsive systems is weakened. The results in this paper allow the coefficient of the derivative of a Lyapunov function to be time-varying function which can be both positive and negative and may even be unbounded. Furthermore, the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and large enough upper bound simultaneously. As a by-product, a unified criterion on ISS for time-varying impulsive delay-free systems is also presented. Two examples are presented to illustrate the effectiveness of our results.
Keywords: Time-varying impulsive delayed systems; Input-to-state stability; Razumikhin-type criterion

Timothy H. Hughes,
On the internal signature and minimal electric network realizations of reciprocal behaviors,
Systems & Control Letters,
Volume 119,
2018,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118301154)
Abstract: In a recent paper, it was shown that (i) any reciprocal system with a proper transfer function possesses a signature-symmetric realization in which each state has either even or odd parity; and (ii) any reciprocal and passive behavior can be realized as the driving-point behavior of an electric network comprising resistors, inductors, capacitors and transformers. These results extended classical results to include uncontrollable systems. In this paper, we establish new lower bounds on the number of states with even parity (capacitors) and odd parity (inductors) for reciprocal systems that need not be controllable.
Keywords: Reciprocity; Passive system; Linear system; Controllability; Observability; Behaviors

György Lipták, Katalin M. Hangos, Mihály Pituk, Gábor Szederkényi,
Semistability of complex balanced kinetic systems with arbitrary time delays,
Systems & Control Letters,
Volume 114,
2018,
Pages 38-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.008.
(http://www.sciencedirect.com/science/article/pii/S016769111830029X)
Abstract: In this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems. We prove the uniqueness of equilibrium solutions within the time delayed positive stoichiometric compatibility classes for such models. In our main result we prove the semistability of the equilibrium solutions for complex balanced systems with arbitrary time delays using an appropriate Lyapunov–Krasovskii functional and LaSalle’s invariance principle. As a consequence, we obtain that every positive complex balanced equilibrium solution is locally asymptotically stable relative to its positive stoichiometric compatibility class.
Keywords: Nonnegative systems; Kinetic systems; Chemical reaction networks; Stability theory; Time delay; Logarithmic Lyapunov–Krasovskii functionals

Andrii Mironchenko, Fabian Wirth,
Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces,
Systems & Control Letters,
Volume 119,
2018,
Pages 64-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118301312)
Abstract: We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions of coercive and non-coercive ISS Lyapunov functions for input-to-state stable linear systems.
Keywords: Nonlinear control systems; Infinite-dimensional systems; Input-to-state stability; Lyapunov methods

João Fábio S. dos Santos, Paulo C. Pellanda, Alberto M. Simões,
Robust pole placement under structural constraints,
Systems & Control Letters,
Volume 116,
2018,
Pages 8-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118300586)
Abstract: A new controller synthesis technique is presented which allows the design of output feedback control systems achieving robust regional pole clustering in the presence of parametric uncertainties as well as satisfying prescribed structural constraints. Such features are rarely jointly present in currently available controller synthesis methods. The central idea in the proposed approach consists in reformulating the original robust pole placement problem into an equivalent robust stabilization problem involving highly structured controller and uncertainty. A numerical application corroborating the applicability of the proposed synthesis technique is also presented.
Keywords: Pole placement; Structured controller; Robust control; Nonsmooth optimization

Mehdi Sadeghpour, Gábor Orosz,
Can a finite number of discrete delays approximate stochastic delay?,
Systems & Control Letters,
Volume 116,
2018,
Pages 27-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300720)
Abstract: In stability analysis and control design for a system with stochastic delay, it is a question whether one can approximate the stochastic system, for instance in the sense of average, with a deterministic system that has a finite number of discrete delay terms with the same delays that appear in the stochastic system and the weight coefficients of these delayed terms are taken from the probability distribution function of the stochastic delay. In this note, we consider a linear system with stochastic delay and discuss conditions under which this approximation is valid and conditions where it is not. In particular, we assume that the delay has piece-wise constant realizations with constant dwelling time at each value and show that the above mentioned approximation loses its grounds when the delay dwelling time gets larger than the minimum delay in the system.
Keywords: Stochastic delay; Discrete delay; Stability; Linear systems

Yirmeyahu J. Kaminski, Jean Lévine, François Ollivier,
Intrinsic and apparent singularities in differentially flat systems, and application to global motion planning,
Systems & Control Letters,
Volume 113,
2018,
Pages 117-124,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.013.
(http://www.sciencedirect.com/science/article/pii/S0167691118300203)
Abstract: In this paper, we study the singularities of differentially flat systems, in the perspective of providing global or semi-global motion planning solutions for such systems: flat outputs may fail to be globally defined, thus potentially preventing from planning trajectories leaving their domain of definition, the complement of which we call singular. Such singular subsets are classified into two types: apparent and intrinsic. A rigorous definition of these singularities is introduced in terms of atlas and local charts in the framework of the differential geometry of jets of infinite order and Lie–Bäcklund isomorphisms. We then give an inclusion result allowing to effectively compute all or part of the intrinsic singularities. Finally, we show how our results apply to the global motion planning of the celebrated example of non holonomic car.
Keywords: Differential flatness; Jets of infinite order; Lie–Bäcklund isomorphism; Atlas; Local chart; Apparent and intrinsic singularity; Global motion planning

Zbigniew Bartosiewicz,
Positive realizations of nonlinear input–output discrete-time systems,
Systems & Control Letters,
Volume 115,
2018,
Pages 9-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118300446)
Abstract: The problem of realization of a positive nonlinear input–output discrete-time system as a positive state-space system is investigated. The input–output system is given by a difference equation of a higher order. A necessary and sufficient condition for existence of positive and regularly positively observable realization is provided. The state space variables of the realization are found as independent generators of some positive universe associated to the input–output system. Only the single-input single-output case is studied and all functions describing the systems and their properties are assumed to be continuous.
Keywords: Nonlinear positive discrete-time system; Input–output system; Positive realization; Regular positive observability

Zhenhua Wang, Cheng-Chew Lim, Yi Shen,
Interval observer design for uncertain discrete-time linear systems,
Systems & Control Letters,
Volume 116,
2018,
Pages 41-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300689)
Abstract: This paper proposes a novel interval observer design method for discrete-time linear systems with unknown but bounded disturbance and measurement noise. The proposed interval observer has a new structure that provides more design degrees of freedom. A direct method based on H∞ technique is used to improve the accuracy of interval estimation. The design conditions are formulated into linear matrix inequalities, which can be efficiently solved. Two numerical examples are given to illustrate the design and validate the performance of the interval observers.
Keywords: Interval observer; Discrete-time; Linear systems; Linear matrix inequalities

Mohamed-Ali Belabbas, Xudong Chen,
Sensor placement for optimal estimation of vector-valued diffusion processes,
Systems & Control Letters,
Volume 121,
2018,
Pages 24-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118301658)
Abstract: Diffusion processes are commonplace in many scientific disciplines, as they describe a broad range of physical phenomenon. Consider a diffusion process observed through linear sensors with additive white noise. We derive the optimal placement of these sensors for estimating this process, where optimality is defined in terms of the mean squared estimation error (MSE) of the state given past observations. We consider two cases. First, we assume the sensors to be orthogonal. We show in this case that the minimum MSE is related to the nuclear norm of the system matrix of the process. Second, we remove the orthogonality constraint and show that the MSE is related to the Schatten p-norm of the system matrix of the process and the optimal sensors are proportional its matrix cube root. We present simulation results illustrating the fact that the gain afforded by optimizing the choice of sensors depends on the ratio p∕n, where n is the dimension of the system and p the dimension of the Wiener processes driving it, and this gain is in general large, especially when p∕n is small.
Keywords: Sensor design; Estimation; Wiener process

Xiaodi Li, Peng Li, Qing-guo Wang,
Input/output-to-state stability of impulsive switched systems,
Systems & Control Letters,
Volume 116,
2018,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118300604)
Abstract: This paper studies the input/output-to-state stability (IOSS) of impulsive switched systems. With the help of Lyapunov and average dwell-time (ADT) methods, some sufficient conditions for IOSS of impulsive switched systems are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. It is shown that when all of the modes are IOSS, a switched system under an ADT scheme is IOSS even if there exist destabilizing impulses, and when none of the modes is IOSS, IOSS can still be achieved under the designed ADT scheme coupled with stabilizing impulses. In particular, for a special case in which an impulsive switched system is composed of some IOSS modes and some non-IOSS modes, a relationship is established among the ADT scheme, impulses, and the total dwell time between non-IOSS and IOSS modes such that the impulsive switched system is IOSS. Two examples are provided to illustrate the applications of our results.
Keywords: Input/output-to-state stability (IOSS); Impulsive switched systems; Average dwell-time (ADT); Lyapunov method

Yonggang Li, Yi Huang, Peng Lin, Wei Ren,
Distributed rotating consensus of second-order multi-agent systems with nonuniform delays,
Systems & Control Letters,
Volume 117,
2018,
Pages 18-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118300690)
Abstract: In this paper, we study a distributed rotating consensus problem of second-order multi-agent systems with nonuniform delays. A distributed algorithm is adopted to drive all agents to reach consensus while moving around a common point. Based on a frequency domain approach, an upper bound on the maximum delay is given for the consensus stability of the system. Finally, a numerical simulation result is included to illustrate the obtained results.
Keywords: Rotating consensus; Nonuniform delays; Multi-agent systems

Hui Liu, Zhiyun Lin, Ming Cao, Xiaoping Wang, Jinhu Lü,
Coordinate-free formation control of multi-agent systems using rooted graphs,
Systems & Control Letters,
Volume 119,
2018,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118301142)
Abstract: This paper studies how to control large formations of autonomous agents in the plane, assuming that each agent is able to sense relative positions of its neighboring agents with respect to its own local coordinate system. We tackle the problem by adopting two types of controllers. First, we use the classical gradient-based controllers on three leader agents to meet their distance constraints. Second, we develop other type of controllers for follower agents: utilizing the properties of rooted graphs, one is able to design linear controllers incorporating relative positions between the follower agents and their neighbors, to stabilize the overall large formations. The advantages of the proposed method are fourfold: (i) fewer constraints on neighboring relationship graphs; (ii) simplicity of linear controllers for follower agents; (iii) global convergence of the overall formations; (iv) implementation in local coordinate systems, in no need of a global coordinate system. Numerical simulations show the effectiveness of the proposed method.
Keywords: Multi-agent system; Formation control; Graph theory; Stabilization

Martin Redmann, Patrick Kürschner,
An output error bound for time-limited balanced truncation,
Systems & Control Letters,
Volume 121,
2018,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.08.004.
(http://www.sciencedirect.com/science/article/pii/S016769111830149X)
Abstract: When solving partial differential equations numerically, usually a high order spatial discretization is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is balanced truncation (BT). However, if one aims at finding a good ROM on a certain finite time interval only, time-limited BT (TLBT) can be a more accurate alternative. So far, no error bound on TLBT has been proved. In this paper, we close this gap in the theory by providing an output error bound for TLBT with two different representations. The performance of the error bound is then shown in several numerical experiments.
Keywords: Model reduction; Linear systems; Time-limited balanced truncation; Time-limited Gramians; Error bound

Maria Elena Valcher, Irene Zorzan,
State–feedback stabilization of multi-input compartmental systems,
Systems & Control Letters,
Volume 119,
2018,
Pages 81-91,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118301300)
Abstract: In this paper we address the positive (state–feedback) stabilization of multi-input compartmental systems, i.e. the design of a state–feedback matrix that preserves the compartmental property of the resulting feedback system, while achieving stability. We first provide necessary and sufficient conditions for the positive stabilizability of compartmental systems whose state matrix is irreducible. Then we address the case when the state matrix is reducible, identify two sufficient conditions for the problem solution, and then extend them to a general algorithm that allows to verify when the problem is solvable and to produce a solution.
Keywords: Compartmental system; Positive (state–feedback) stabilization; Hurwitz matrix; Digraph

Jian Wang,
Stabilization of a discrete time linear system over finite data-rate channel with noise attenuation performance by spherical polar coordinate quantizer,
Systems & Control Letters,
Volume 117,
2018,
Pages 45-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300574)
Abstract: This paper considers the problem of achieving the first moment stability and the given noise attenuation performance of a discrete time linear system with unbounded noise. Based on spherical polar coordinates, a quantizer is proposed with a definite relation between the quantized data and the corresponding quantization error. And a necessary and sufficient condition for the first moment stability of the system is presented. Further, based on the quantizer, two coding schemes are proposed for time-varying data rate and fixed data rate respectively, which achieve both the first moment stability and the noise attenuation performance of the system with unbounded noise.
Keywords: Unbounded noise; First moment stability; Noise attenuation; Finite data-rate channel

Yan-Qiao Wei, Da-Yan Liu, Driss Boutat, Yi-Ming Chen,
An improved pseudo-state estimator for a class of commensurate fractional order linear systems based on fractional order modulating functions,
Systems & Control Letters,
Volume 118,
2018,
Pages 29-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.011.
(http://www.sciencedirect.com/science/article/pii/S0167691118301026)
Abstract: In this paper, a non-asymptotic pseudo-state estimator for a class of commensurate fractional order linear systems is designed in noisy environment. Different from existing modulating functions methods, the proposed method is based on the system model with fractional sequential derivatives by introducing fractional order modulating functions. By applying the fractional order integration by parts formula and thanks to the properties of the fractional order modulating functions, a set of fractional derivatives and fractional order initial values of the output are analogously obtained by algebraic integral formulas. Then, an explicit formula of the pseudo-state is accomplished by using the fractional sequential derivatives of the output computed based on the previous results. This formula does not contain any source of errors in continuous noise-free case, and can be used to non-asymptotically estimate the pseudo-state in discrete noisy case. The construction of the fractional order modulating functions is also shown, which is independent of the time. Finally, simulations and comparison results demonstrate the efficiency and robustness of the proposed method.
Keywords: Non-asymptotic method; Fractional order modulating functions; Robust estimation; Pseudo-state estimator; Fractional derivative initial values

Xiang Yin, Zhaojian Li, Weilin Wang,
Trajectory detectability of discrete-event systems,
Systems & Control Letters,
Volume 119,
2018,
Pages 101-107,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118301324)
Abstract: We investigate the trajectory estimation problem for partially-observed discrete event systems. In some applications, only knowing the current state of the system may be insufficient, and knowing which trajectory the system takes to reach the current state could be important. This requires more precise knowledge about the system. In this paper, a language-based framework is proposed in order to tackle this problem. Two new notions of detectability, called trajectory detectability and periodic trajectory detectability, are proposed to capture different requirements in the aforementioned trajectory estimation problem. Effective verification algorithms are also provided. Our results extend the theory on detectability of discrete event systems from state estimation problem to trajectory estimation problem.
Keywords: Discrete-event systems; Trajectory estimation; Detectability

Yuta Yaegashi, Hidekazu Yoshioka,
Unique solvability of a singular stochastic control model for population management,
Systems & Control Letters,
Volume 116,
2018,
Pages 66-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118300598)
Abstract: We present and mathematically analyze a singular stochastic control model for cost-effective and ecologically-sound indirect population control strategy for fish-eating birds. Finding the optimal strategy of a threshold type reduces to solving a variational inequality. We prove the unique existence of its viscosity solution that is neither convex nor concave, which turns out to be a classical solution. Comparative statics on the optimal threshold is performed as well to demonstrate practical implications of the model.
Keywords: Indirect population control; Singular stochastic control; Variational inequality; Viscosity solution; Classical solution

Daizhan Cheng, Changxi Li, Fenghua He,
Observability of Boolean networks via set controllability approach,
Systems & Control Letters,
Volume 115,
2018,
Pages 22-25,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.03.004.
(http://www.sciencedirect.com/science/article/pii/S016769111830046X)
Abstract: Controllability and observability of Boolean control networks (BCNs) are two fundamental properties. But verification of the latter is much harder than the former. This paper considers the observability of BCNs via controllability. First, set controllability is proposed, and a necessary and sufficient condition is obtained. Then a technique is developed to convert observability into an equivalent set controllability problem. Using the result for set controllability, a necessary and sufficient condition is also obtained for the observability of BCNs.
Keywords: Boolean control networks; Set controllability; Observability; Semi-tensor product of matrices

Yongqiang Guan, Long Wang,
Controllability of multi-agent systems with directed and weighted signed networks,
Systems & Control Letters,
Volume 116,
2018,
Pages 47-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118300756)
Abstract: This paper studies the controllability of multi-agent systems with signed networks, which are represented by directed weighted signed graphs. The adjacency weights of network depict the property of interactions. Positive weight means cooperative interaction while negative weight antagonistic interaction. First, by using switching equivalent transformation, the controllability of three kinds of signed networks is studied: structurally balanced, anti-balanced, and strictly unbalanced. It is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network. Then, a graph-theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks. Furthermore, some necessary and sufficient conditions are given for the controllability of generic linear multi-agent systems. In addition, several examples are presented to illustrate the theoretical results.
Keywords: Multi-agent systems; Controllability; Directed weighted signed networks; Almost equitable partition

Shuzhen Yang,
The necessary and sufficient conditions for stochastic differential systems with multi-time state cost functional,
Systems & Control Letters,
Volume 114,
2018,
Pages 11-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118300239)
Abstract: From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with multi-time state cost functional. By constructing a series of first-order adjoint equations, we establish the stochastic maximum principle and sufficient optimality conditions for this new optimal control problem. A constrained problem also be studied. In the end, we develop a near optimal control problem for a general cost functional.
Keywords: Stochastic differential equations; Stochastic maximum principle; Constrained conditions

Ryan Murray, Michele Palladino,
A model for system uncertainty in reinforcement learning,
Systems & Control Letters,
Volume 122,
2018,
Pages 24-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.011.
(http://www.sciencedirect.com/science/article/pii/S0167691118301725)
Abstract: This work provides a rigorous framework for studying continuous-time control problems in uncertain environments. The framework models uncertainty in state dynamics as a probability measure on the space of functions. Such a probability measure is permitted to change over time as agents learn about their environment. This model can be seen as a variant of either Bayesian reinforcement learning (RL) or adaptive optimal control. We study conditions for locally optimal trajectories within this model, in particular deriving an appropriate dynamic programming principle and Hamilton–Jacobi equations. Some discussion of variants of the model are also provided, including one potential framework for studying the tradeoff between exploration and exploitation in RL.
Keywords: Dynamic programming; Learning systems; Machine learning; Adaptive control

Grace S. Deaecto, José C. Geromel,
Stability and performance of discrete-time switched linear systems,
Systems & Control Letters,
Volume 118,
2018,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118300914)
Abstract: This paper deals with stability analysis and control design of discrete-time switched linear systems. The results are based on a new sufficient condition for exponential stabilizability. A performance index that falls in the context of H2 norm is considered in order to optimize the joint design of a state dependent switching function and a state feedback control law. All control design conditions are expressed through linear matrix inequalities (LMIs). Comparisons with other available design procedures are made by means of examples borrowed from the literature. The present procedure is more amenable for control synthesis purposes and simpler from both theoretical and numerical viewpoints. Three state feedback control switching strategies are presented. The complexity of the control law is discussed.
Keywords: Switched linear systems; Stability analysis; 
               H2 control design

Wei Zhang, Jr-Shin Li,
On controllability of time-varying linear population systems with parameters in unbounded sets,
Systems & Control Letters,
Volume 118,
2018,
Pages 94-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.014.
(http://www.sciencedirect.com/science/article/pii/S0167691118301051)
Abstract: The ability to finely manipulate a population of structurally identical dynamical systems is important for various emerging applications across a broad spectrum of fields in science and engineering. Robust control of such an ensemble is fundamentally challenging, because individual systems in the ensemble obey the same dynamical law but have different system parameter values, and only a broadcast control can be applied to the entire ensemble. In this paper, we establish controllability conditions for the finite-dimensional time-varying linear ensemble system in a Hilbert space, whose parameters are in an unbounded set. This work extends our previous study in one-parameter families of linear ensemble systems with the parameter lying in a one-dimensional compact set.
Keywords: Ensemble control; Population systems; Parameter-dependent systems; Singular systems; Hilbert–Schmidt operators

Xue Luo, Xiuqiong Chen, Stephen S.-T. Yau,
Suboptimal linear estimation for continuous–discrete bilinear systems,
Systems & Control Letters,
Volume 119,
2018,
Pages 92-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118301294)
Abstract: In this paper we derive a suboptimal estimation for continuous–discrete bilinear systems. One of the motivations of this work is that the bilinear system has the simplest structure in the nonlinear class in some sense. Similar to the Kalman filter, our algorithm includes prediction and updating step. We show rigorously that our algorithm gives an unbiased estimate, the a-priori estimate approaches to the conditional expectation exponentially fast, and the posterior estimate minimizes the conditional variance error in the linear space spanned by the a-priori estimate and the innovation. Our algorithm is also applicable to solve the nonlinear filtering problems. The efficiency of our method is illustrated by the cubic sensor problem and Lorenz system with discrete observation. The results have been compared with the extended Kalman filter and the unscented Kalman filter.
Keywords: Nonlinear filtering; Bilinear systems; Carleman approach; The extended Kalman filter

H. Hammouri, F.S. Ahmed, S. Othman,
Observer design based on immersion technics and canonical form,
Systems & Control Letters,
Volume 114,
2018,
Pages 19-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300240)
Abstract: A crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system, and the analytical expression of the inverse of the immersion is unknown. In this paper, we have proposed a method for constructing observers for such autonomous nonlinear systems.
Keywords: Nonlinear system; Immersion; Observer

Arjan van der Schaft, Bernhard Maschke,
Generalized port-Hamiltonian DAE systems,
Systems & Control Letters,
Volume 121,
2018,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118301695)
Abstract: Motivated by recent work in this area we expand on a generalization of port-Hamiltonian systems that is obtained by replacing the Hamiltonian function representing energy storage by a Lagrangian subspace. This leads to a new class of algebraic constraints and DAE systems in physical systems modeling. It is shown how Dirac structures and Lagrangian subspaces allow for similar representations, and how this can be exploited to convert algebraic constraints originating from Dirac structures into algebraic constraints corresponding to Lagrangian subspaces, and conversely.
Keywords: Port-Hamiltonian system; Algebraic constraint; Dirac structure; Lagrangian subspace; DAE system

Mohammad Ali Golkani, Stefan Koch, Markus Reichhartinger, Martin Horn,
A novel saturated super-twisting algorithm,
Systems & Control Letters,
Volume 119,
2018,
Pages 52-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118301178)
Abstract: In this paper, a feedback control law adopting the super-twisting algorithm is designed such that a continuous and saturated control signal is generated to regulate a first-order system affected by disturbances. For the unperturbed as well as perturbed systems under the proposed control law, global finite-time stability properties are established. In order to indicate the feasibility and effectiveness of the approach, numerical simulations are employed.
Keywords: Saturated sliding mode control; Continuous actuating signal

Zhe Wu, Helen Durand, Panagiotis D. Christofides,
Safe economic model predictive control of nonlinear systems,
Systems & Control Letters,
Volume 118,
2018,
Pages 69-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.013.
(http://www.sciencedirect.com/science/article/pii/S016769111830104X)
Abstract: This work focuses on the design of a new class of economic model predictive control (EMPC) systems for nonlinear systems that address simultaneously the tasks of economic optimality, safety and closed-loop stability. This is accomplished by incorporating in the EMPC an economics-based cost function and Control Lyapunov-Barrier Function (CLBF)-based constraints that ensure that the closed-loop state does not enter unsafe sets and remains within a well-characterized set in the system state-space. The new class of CLBF-EMPC systems is demonstrated using a nonlinear chemical process example.
Keywords: Process operational safety; Model predictive control; Control Lyapunov-barrier functions; Nonlinear systems; Chemical processes

Iasson Karafyllis, Miroslav Krstic,
Small-gain stability analysis of certain hyperbolic–parabolic PDE loops,
Systems & Control Letters,
Volume 118,
2018,
Pages 52-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118301038)
Abstract: This work provides stability results in the spatial sup norm for hyperbolic–parabolic loops in one spatial dimension. The results are obtained by an application of the small-gain stability analysis. Two particular cases are selected for the study because they contain challenges typical of more general systems (to which the results are easily generalizable but at the expense of less pedagogical clarity and more notational clutter): (i) the feedback interconnection of a parabolic PDE with a first-order zero-speed hyperbolic PDE with boundary disturbances, and (ii) the feedback interconnection, by means of a combination of boundary and in-domain terms, of a parabolic PDE with a first-order hyperbolic PDE. The first case arises in the study of the movement of chemicals underground and includes the wave equation with Kelvin–Voigt damping as a subcase. The second case arises when we apply backstepping to a pair of hyperbolic PDEs that is obtained by ignoring diffusion phenomena. Moreover, the second case arises in the study of parabolic PDEs with distributed delays. In the first case, we provide sufficient conditions for ISS in the spatial sup norm with respect to boundary disturbances. In the second case, we provide (delay-independent) sufficient conditions for exponential stability in the spatial sup norm.
Keywords: ISS; Parabolic PDEs; Hyperbolic PDEs; Boundary disturbances

Alexis J. Vallarella, Hernan Haimovich,
Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems,
Systems & Control Letters,
Volume 122,
2018,
Pages 60-66,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118301798)
Abstract: Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.
Keywords: Sampled-data; Nonlinear systems; Non-uniform sampling; Input-to-state stability (ISS); Discrete-time models

Mahdi Abolhasani, Mehdi Rahmani,
Robust deterministic least-squares filtering for uncertain time-varying nonlinear systems with unknown inputs,
Systems & Control Letters,
Volume 122,
2018,
Pages 1-11,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.005.
(http://www.sciencedirect.com/science/article/pii/S016769111830166X)
Abstract: The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches.
Keywords: Robust deterministic filtering; Two-stage filtering; Regularized least-squares problem; Nonlinear systems; Unknown inputs

Jingfang Huang, Xin Yu, Kangsheng Liu,
Semidiscrete finite element approximation of time optimal control problems for semilinear heat equations with nonsmooth initial data,
Systems & Control Letters,
Volume 116,
2018,
Pages 32-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118300744)
Abstract: This paper is devoted to the study of semidiscrete finite element approximation of time optimal control problem governed by semilinear heat equation with nonsmooth initial data. When the control is acted locally, an error estimate for the optimal time is obtained by making use of the approximation results for the equations. Moreover, with the help of Pontryagin’s maximum principle and the unique continuation property for the heat equation, a better error estimate for the optimal time can be derived when the control is acted globally into the state equation.
Keywords: Time optimal control; Finite element approximation; Error estimate; Pontryagin’s maximum principle; Unique continuation

E. Bakolas,
Constrained minimum variance control for discrete-time stochastic linear systems,
Systems & Control Letters,
Volume 113,
2018,
Pages 109-116,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118300227)
Abstract: We propose a computational scheme for the solution of the so-called minimum variance control problem for discrete-time stochastic linear systems subject to an explicit constraint on the 2-norm of the input (random) sequence. In our approach, we utilize a state space framework in which the minimum variance control problem is interpreted as a finite-horizon stochastic optimal control problem with incomplete state information. We show that if the set of admissible control policies for the stochastic optimal control problem consists exclusively of sequences of causal (non-anticipative) control laws that can be expressed as linear combinations of all the past and present outputs of the system together with its past inputs, then the stochastic optimal control problem can be reduced to a deterministic, finite-dimensional optimization problem. Subsequently, we show that the latter optimization problem can be associated with an equivalent convex program and in particular, a quadratically constrained quadratic program (QCQP), by means of a bilinear transformation. Finally, we present numerical simulations that illustrate the key ideas of this work.
Keywords: Minimum-variance control; Stochastic optimal control; Discrete-time stochastic systems; Convex optimization

Haofei Meng, Zhiyong Chen,
Input-to-state stability of switched systems with explicit gain functions,
Systems & Control Letters,
Volume 122,
2018,
Pages 39-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118301713)
Abstract: Input-to-state stability (ISS) for a switched system is a stronger property than stability in characterizing the external influence on system performance. In this paper, we study ISS for a linear switched system with marginally stable subsystems and hence with polynomially unstable subsystems. Moreover, we aim to calculate an explicit ISS gain which is critical in explicit controller design when the linear switched system is incorporated with other dynamic behavior in a complicated large-scale structure.
Keywords: Input-to-state stability; Switched systems; Lyapunov function; Linear systems; Multi-agent systems

Chan-eun Park, Nam Kyu Kwon, PooGyeon Park,
Optimal H∞ filtering for singular Markovian jump systems,
Systems & Control Letters,
Volume 118,
2018,
Pages 22-28,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300902)
Abstract: This paper considers H∞ filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H∞ filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H∞ filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H∞ filtering.
Keywords: 
               H∞ filtering; Linear matrix inequality; Singular Markovian jump system

Hossein Beikzadeh, Guangjun Liu, Horacio J. Marquez,
Robust sensitive fault detection and estimation for single-rate and multirate nonlinear sampled-data systems,
Systems & Control Letters,
Volume 119,
2018,
Pages 71-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118301282)
Abstract: This paper investigates the problem of fault detection and estimation for nonlinear sampled-data systems in the presence of unknown exogenous inputs. Both cases of single-rate and multirate sampling are treated and general observer-based frameworks are provided using discrete-time approximation to estimate fault signals of any sources. We show that these frameworks are input-to-error stable with respect to the estimation error and can simultaneously enhance robustness against unknown inputs and sensitivity to faults in a mixed H−∕H∞ sense for the unknown exact discrete-time model of the plant. Our results are then applied to a class of Lipschitz nonlinear systems with a refined Euler approximate model to derive sampled-data fault estimation techniques where stability and H−∕H∞ optimization are ensured using linear matrix inequalities (LMIs). Simulation results of a flexible joint robot illustrate the effectiveness of the proposed methodologies.
Keywords: Fault estimation; Nonlinear sampled-data systems; Input-to-error stable; 
               H−∕H∞ optimization; Lipschitz condition; Linear matrix inequality (LMI); Multirate sampling

Ramin Esmzad, Reza Mahboobi Esfanjani,
Modified likelihood Kalman filter for systems with incomplete, delayed and lost measurements,
Systems & Control Letters,
Volume 120,
2018,
Pages 23-28,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.08.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118301440)
Abstract: In this note, a novel Kalman filter is developed in the Bayesian framework for linear dynamical systems whose outputs are measured by faulty sensors and transmitted to the filter through a lossy delaying channel. The main novelty of the proposed method is to modify the likelihood function of the common Kalman filter to cope with incomplete, delayed and lost measurements. The suggested modified likelihood filter can be interpreted as an adaptive Kalman filter, wherein weighting factors are tuned based on the characteristics of the received measurements. Estimation accuracy is assured provided that some conditions on the properties of the sensor and the channel are met. Simulation results are presented to demonstrate the superior performance of the introduced filter compared to some rival ones in the literature.
Keywords: Bayesian filter; Likelihood function; Incomplete information; Transmission delay; Data dropout

Xiao Liang, Juanjuan Xu, Huanshui Zhang,
Solution to stochastic LQ control problem for Itô systems with state delay or input delay,
Systems & Control Letters,
Volume 113,
2018,
Pages 86-92,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118300197)
Abstract: This paper is concerned with the linear quadratic (LQ) control problem for Itô stochastic systems with state delay or input delay. The main contribution is to give the explicit optimal LQ controllers for Itô stochastic systems with input delay and with state delay respectively. For the case of state delay, the optimal LQ controller is a linear function of the state at the current time and the past time. For the case of input delay, the optimal LQ controller is a linear function of the state and the past inputs. The key technology is to define the value function and complete the square based on the coupled differential equations.
Keywords: LQ control; State delay; Input delay; Itô stochastic system; Value function

Jacob van der Woude, Taha Boukhobza, Christian Commault,
On structural behavioural controllability of linear discrete time systems with delays,
Systems & Control Letters,
Volume 119,
2018,
Pages 31-38,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.06.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118301166)
Abstract: In this paper we study the controllability of interconnected networks that are described by means of structured linear systems with state-like and control variables. We assume that the systems operate in discrete time with the set of integers as the time axis. Further, we assume that the state-like variables for their evolution only depend on recent values of their neighbours with, however, unknown weight factors. These recent values may be one step back in time, but also more steps. This yields a description of the systems by means of matrices containing fixed zeros and free parameters, together with a time lag structure. Knowing the dependency and lag structure, we represent (the structure of the) systems by means of weighted directed graphs and study questions concerning their structural controllability, where the latter has to be defined in an appropriate way, i.e., in behavioural sense. We provide a necessary and sufficient characterization of structural controllability of our systems using a graph representation. The obtained characterization makes use of well-known and efficient algorithms from graph theory. We prove that in this context finding the minimal number of driver (controller) nodes is an NP-hard problem. The concepts and results of the paper are illustrated on academic examples and on a gene regulatory network.
Keywords: Linear discrete time models; Structured systems; Behavioural controllability; Graph theory

Quanxin Zhu,
Stability analysis of stochastic delay differential equations with Lévy noise,
Systems & Control Letters,
Volume 118,
2018,
Pages 62-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.015.
(http://www.sciencedirect.com/science/article/pii/S0167691118301105)
Abstract: This paper is concerned with pth moment exponential stability problem for a class of stochastic delay differential equations driven by Lévy processes. Several new stability theorems are obtained by developing a method—proof by contradiction. Moreover, the results are applied to investigate the pth moment exponential stability of stochastic neural networks with Lévy noise. In particular, the time-varying delay in our results is not required to be differentiable, even not continuous. The obtained results improve greatly some previous works given in the literature. In particular, our method can easily correct the incorrect proofs appeared in two recent papers. Finally, two examples are provided to show the effectiveness of the theoretical results.
Keywords: Stochastic delay differential equation; Neural network; Time-varying delay; 
               pth moment exponential stability; Lévy noise

D. Bauso,
Nonlinear network dynamics for interconnected micro-grids,
Systems & Control Letters,
Volume 118,
2018,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.014.
(http://www.sciencedirect.com/science/article/pii/S0167691118300896)
Abstract: This paper deals with transient stability in interconnected micro-grids. The main challenge is to understand the impact of the connectivity of the graph and model nonlinearities on transient and steady-state behavior of the system as a whole. The contribution of this paper is three-fold. First, we provide a robust classification of transient dynamics for different intervals of the parameters for a single micro-grid. We prove that underdamped dynamics and oscillations arise when the damping coefficient is below a certain threshold which we calculate explicitly as function of the product between the inertia coefficient and the synchronization parameter. Second, for interconnected micro-grids, under the hypothesis of homogeneity, we prove that the transient dynamics mimics a consensus dynamics. We provide bounds on the damping coefficient characterizing underdamped and overdamped consensus. Third, we extend the study to the case of disturbed measurements due to hackering or parameter uncertainties. We introduce model nonlinearities and prove absolute stability.
Keywords: Synchronization; Consensus; Transient stability

Kai Zhao, Yongduan Song, Jiye Qian, Jin Fu,
Zero-error tracking control with pre-assignable convergence mode for nonlinear systems under nonvanishing uncertainties and unknown control direction,
Systems & Control Letters,
Volume 115,
2018,
Pages 34-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118300379)
Abstract: This work addresses the tracking control problem for a class of high-order multi-input multi-output (MIMO) nonlinear systems with unknown control direction and nonparametric uncertainties. By integrating a matrix (rather than scalar) rate transformation with Nussbaum gain, we develop an accelerated robust adaptive control that exhibits several attractive features: (1) it is able to achieve full-state zero-error tracking despite unknown control direction and non-vanishing uncertainties; (2) with the proposed control scheme, the whole tracking process seamlessly consists of the first phase of steering the tracking error into an adjustable small residual region with accelerated convergence rate and the second phase of further driving the error to zero; (3) before reaching the residual region, each component of the tracking error is forced to decay at an accelerated rate that can be pre-assigned; and (4) the resultant control action is continuous differentiable everywhere without involving excessively large initial driving effort.
Keywords: Accelerated tracking; MIMO nonlinear systems; Matrix rate transformation; Unknown control direction

Victor Ayala, Philippe Jouan,
Singular linear systems on Lie groups; equivalence,
Systems & Control Letters,
Volume 120,
2018,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118301348)
Abstract: In this paper, we define different kinds of singular systems on Lie groups and we analyze some of them. Furthermore, we state sufficient conditions for a general nonlinear singular system defined on a manifold to be equivalent by diffeomorphism to one of these models. Some examples are computed.
Keywords: Singular systems; Control systems; Lie groups; Homogeneous spaces

I. Pontes Duff, C. Poussot-Vassal, C. Seren,
H2-optimal model approximation by input/output-delay structured reduced order models,
Systems & Control Letters,
Volume 117,
2018,
Pages 60-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300811)
Abstract: In this paper, the H2-optimal approximation of a multi-input multi-output transfer function by a finite dimensional system including input/output delays, is addressed. This problem is of particular interest when the full order model represents a transport phenomenon. The contribution is twofold : firstly, based on the pole/residue decomposition, an H2-inner product formula in the presence of input/output delays is derived. Secondly, the underlying H2 optimality conditions of the approximation problem are obtained as an extension of the tangential interpolatory conditions. It is also demonstrated that for fixed delay values, this problem can be recast as a rational function approximation one. An iterative algorithm is sketched out and numerical results assess the theoretical contributions.
Keywords: Model reduction; Time-delay systems; Large-scale systems; Linear systems

Tianrui Zhao, Bin Zhou, Wim Michiels,
Stability analysis of linear time-varying time-delay systems by non-quadratic Lyapunov functions with indefinite derivatives,
Systems & Control Letters,
Volume 122,
2018,
Pages 77-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118301749)
Abstract: This paper presents a stability analysis of linear time-varying (LTV) time-delay systems by using non-quadratic Lyapunov functions and functionals. Two types of sufficient conditions are proposed for testing several different kinds of stability, such as asymptotic stability, exponential stability and uniformly exponential stability, for LTV systems without delay. Then, by constructing suitable non-quadratic Lyapunov functions (functionals) that are respectively the time-varying weighted L1 and L∞ norms of the state variables and by using properties of the uniformly asymptotically stable (UAS) function and the recently established improved Razumikhin and Krasovskii stability theorems, both delay-dependent and delay-independent conditions are proposed for testing uniformly exponential stability of a class of LTV time-delay systems. The time derivatives of the non-quadratic Lyapunov functions (functionals) along the solutions are allowed to be indefinite, namely, to take both negative and positive values. Numerical examples show that the non-quadratic Lyapunov functions (functionals) based methods are more efficient than the existing ones that are based on quadratic functions (functionals).
Keywords: Linear time-varying systems; Time-delay systems; Stability analysis; Non-quadratic Lyapunov functions; Indefinite time-derivatives

Y. Shi, H.D. Tuan, P. Apkarian, A.V. Savkin,
Global optimal power flow over large-scale power transmission networks,
Systems & Control Letters,
Volume 118,
2018,
Pages 16-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118300938)
Abstract: Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These computationally intractable constraints are often expressed by linear constraints plus matrix additional rank-one constraints on the outer products of the voltage vectors. The existing convex relaxation technique, which drops the difficult rank-one constraints for tractable computation, cannot yield even a feasible point. We address these computationally difficult problems by an iterative procedure, which generates a sequence of improved points that converges to a rank-one solution. Each iteration calls a semi-definite program. Intensive simulations for the OPF problems over networks with a few thousands of buses are provided to demonstrate the efficiency of our approach. The suboptimal values of the OPF problems found by our computational procedure turn out to be the global optimal value with computational tolerance less than 0.01%.
Keywords: Optimal power flow (OPF) problem; Large-scale transmission networks; Rank-one matrix constraint; Nonsmooth optimization; Semi-definite programming (SDP)

Xiaoquan Tang, Long Zhang,
Stability orthogonal regression for system identification,
Systems & Control Letters,
Volume 117,
2018,
Pages 30-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.002.
(http://www.sciencedirect.com/science/article/pii/S016769111830080X)
Abstract: Variable selection methods have been widely used for system identification. However, there is still a major challenge in producing parsimonious models with optimal model structures as popular variable selection methods often produce suboptimal model with redundant model terms. In the paper, stability orthogonal regression (SOR) is proposed to build a more compact model with fewer or no redundant model terms. The main idea of SOR is that multiple intermediate models are produced by orthogonal forward regression (OFR) using sub-sampling technique and then the final model is a combination of these intermediate model terms but does not include infrequently selected terms. The effectiveness of the proposed methods is analyzed in theory and also demonstrated using two numerical examples in comparison with some popular algorithms.
Keywords: Orthogonal forward regression; Stability selection; Stability orthogonal regression; System identification

Ying Zhao, Dan Ma, Jun Zhao,
L2 bumpless transfer control for switched linear systems with almost output regulation,
Systems & Control Letters,
Volume 119,
2018,
Pages 39-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118301191)
Abstract: In this paper, the issue of L2 bumpless transfer control for switched linear systems with almost output regulation property is investigated. First, a description of the L2 bumpless transfer performance for a category of switched linear systems is given to measure the output bumpless transfer levels of the systems. Then, a compensator and a switching law are designed via a multiple Lyapunov functions strategy. Under the designed compensator and switching law, a sufficient condition guaranteeing the L2 bumpless transfer property and the almost output regulation property of the systems is presented. Furthermore, the sufficient condition allows each subsystem not to have both properties. At last, an example showing the effectiveness of the proposed control scheme is offered by controlling a turbofan model.
Keywords: Switched linear systems; 
               L2 bumpless transfer control; Almost output regulation; Multiple Lyapunov functions strategy

Bernard Vau, Henri Bourlès,
Some remarks on the bias distribution analysis of discrete-time identification algorithms based on pseudo-linear regressions,
Systems & Control Letters,
Volume 119,
2018,
Pages 46-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.002.
(http://www.sciencedirect.com/science/article/pii/S016769111830118X)
Abstract: In 1998, A. Karimi and I.D. Landau published in this journal an article entitled “Comparison of the closed-loop identication methods in terms of bias distribution”. One of its main purposes was to provide a bias distribution analysis in the frequency domain of closed-loop output error identication algorithms that had been recently developed. The expressions provided in that paper are only valid for prediction error identification methods (PEM), not for pseudo-linear regression (PLR) ones, for which we give the correct frequency domain bias analysis, both in open- and closed-loop. Although PLR was initially (and is still) considered as an approximation of PEM, we show that it gives better results at high frequencies.
Keywords: Identification; Recursive identification; Closed-loop identification; Bias analysis

Mojeed O. Oyedeji, Magdi S. Mahmoud,
Couple-group consensus conditions for general first-order multiagent systems with communication delays,
Systems & Control Letters,
Volume 117,
2018,
Pages 37-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.013.
(http://www.sciencedirect.com/science/article/pii/S0167691118300781)
Abstract: In this paper, we establish group consensus conditions for first-order systems with communication delays using the relationship between time-delay parameter and the closed-loop characteristic roots. At first, we derive necessary conditions for the delay-free case, then we proceed to the delay-induced case. Contrary to most studies on group consensus where the conditions are derived considering the Laplacian of the entire multiagent network, we derive the group consensus conditions based on the Laplacian matrices that describe each subgroup and the inter-connection among sub-groups. Simulation studies are used to validate the derived conditions.
Keywords: Communication delay; Laplacian; First-order systems; Group consensus

Jianhui Huang, Haiyang Wang, Zhen Wu,
A sufficient stochastic maximum principle for a kind of recursive optimal control problem with obstacle constraint,
Systems & Control Letters,
Volume 114,
2018,
Pages 27-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300264)
Abstract: In this paper, we study a kind of recursive optimal control problem whose utility functional is described by the solution of a reflected backward stochastic differential equation (BSDE). We obtain a sufficient stochastic maximum principle of optimal controls. Moreover, a mixed optimal control problem is considered to illustrate the application of our theoretical result and the optimal control and stopping strategy are given.
Keywords: Maximum principle; Reflected backward stochastic differential equations; Recursive optimal control problems; Mixed control problems; Clarke’s generalized gradient

Yilun Shang,
Resilient consensus of switched multi-agent systems,
Systems & Control Letters,
Volume 122,
2018,
Pages 12-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.10.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118301750)
Abstract: This letter considers the resilient consensus problem for switched multi-agent systems composed of continuous-time and discrete-time subsystems. We propose a switched filtering strategy for cooperative nodes based upon available local information, withstanding the threat of non-cooperative nodes. We provide conditions that guarantee resilient consensus in the presence of locally bounded Byzantine nodes in directed networks under arbitrary switching. Resilient scaled consensus and resilient scaled formation generation problems for switched multi-agent systems are solved as generalizations. Simulations are also provided to illustrate the effectiveness of the theoretical results.
Keywords: Resilient consensus; Switched multi-agent system; Directed network; Scaled consensus; Formation control

Wentao Tang, Prodromos Daoutidis,
Distributed adaptive dynamic programming for data-driven optimal control,
Systems & Control Letters,
Volume 120,
2018,
Pages 36-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.08.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118301476)
Abstract: Adaptive dynamic programming (ADP), as an important optimal control technique, can be exploited in the setting of data-driven control based on an approximate regression-based solution of the Hamilton–Jacobi–Bellman (HJB) equations. Distributed optimization algorithms, which are extensively studied in statistics and machine learning, have not yet been applied to the solution of data-driven ADP problems. In this work, we identify the data-driven ADP problem as a consensus optimization problem for nonlinear affine systems, and apply the alternating direction method of multipliers (ADMM) and its accelerated variants for its solution. For the input-constrained optimal control problem, we define a combined optimal primal–dual function to develop a data-based version of the input-constrained HJB equation.
Keywords: Data-driven control; Process control; Adaptive dynamic programming; Distributed optimization

Konstantinos B. Liaskos, Athanasios A. Pantelous, Ioannis A. Kougioumtzoglou, Antonios T. Meimaris,
Implicit analytic solutions for the linear stochastic partial differential beam equation with fractional derivative terms,
Systems & Control Letters,
Volume 121,
2018,
Pages 38-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.09.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118301610)
Abstract: Analytic solutions in implicit-form are derived for a linear stochastic partial differential equation (SPDE) with fractional derivative terms, which can model the dynamics of a stochastically excited Euler–Bernoulli beam resting on a viscoelastic foundation. Specifically, the original initial–boundary value problem of the SPDE is reduced to an initial value problem of a second-order stochastic differential equation in an appropriate Hilbert space. Next, addressing the abstract Cauchy problem, employing cosine and sine families of operators, and representing the fractional derivative term in a suitable form, a variation of parameters treatment yields the solution in implicit-form. The limiting purely viscous and purely elastic modeling cases are also studied within the same framework. The herein proposed technique and derived implicit-form solutions can be construed as an extension of available results in the literature to account for fractional derivative terms. This generalization is of significant importance given the vast utilization of fractional calculus modeling in engineering mechanics, and in viscoelastic material behavior in particular. In this regard, the herein proposed analytical treatment also supplements existing more numerically oriented solution schemes available in the engineering mechanics literature.
Keywords: Stochastic partial differential equation; Fractional derivative; Euler–Bernoulli beam; Hilbert space; Implicit analytic solution

Kazuya Takijiri, Hideaki Ishii,
Networked control of uncertain systems via the coarsest quantization and lossy communication,
Systems & Control Letters,
Volume 119,
2018,
Pages 57-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.07.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118301336)
Abstract: We study a networked control problem of uncertain systems based on quantized signals sent over unreliable, lossy communication channels. The coarsest quantization is characterized for attaining the objective of quadratic stability of the overall closed-loop system in a stochastic sense. Our result indicates that the coarsest quantization is given by the logarithmic type and that more information is required through finer quantization for more uncertain systems and more unreliable channels. The characterization provides an analytic upper bound for the coarseness, which is tight for some special cases and generalizes known results for systems without uncertainties and for channels without losses.
Keywords: Networked control; Quantization; System uncertainties; Packet losses; Quadratic stability

N. Noroozi, S.H. Mousavi, H.J. Marquez,
Integral versions of input-to-state stability for dual-rate nonlinear sampled-data systems,
Systems & Control Letters,
Volume 117,
2018,
Pages 11-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.04.011.
(http://www.sciencedirect.com/science/article/pii/S0167691118300768)
Abstract: This paper presents versions of integral input-to-state stability and integral input-to-integral-state stability for nonlinear sampled-data systems, under the low measurement rate constraint. In particular, we compensate the lack of measurements using an estimator approximately reconstructing the current state. Interestingly, under certain checkable conditions, we establish that a controller that semiglobally practically integral input-to-(integral-)state stabilizes an approximate discrete-time model of a single-rate nonlinear sampled-data system, also stabilizes the exact discrete-time model of the nonlinear sampled-data system in the same sense implemented in a dual-rate setting. Numerical simulations are given to illustrate the effectiveness of our results.
Keywords: Sampled-data systems; Discrete-time approach; Lyapunov methods; Input-to-state stability

Hong-feng Tao, Wojciech Paszke, Eric Rogers, Krzysztof Gałkowski, Hui-zhong Yang,
Modified Newton method based iterative learning control design for discrete nonlinear systems with constraints,
Systems & Control Letters,
Volume 118,
2018,
Pages 35-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.05.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300926)
Abstract: This paper considers the design of iterative learning control laws for classes of nonlinear dynamics. In particular, a new Newton method design is developed for discrete nonlinear systems in the presence of input constraints, where such constraints will arise in applications. The new design is based on the use of a penalty function and an iterative method for solving an unconstrained nonlinear optimization problem with an algorithm that has monotonic and super linear convergence characteristics. In this new algorithm the input inequality constraints are transformed into equality form by adding auxiliary variables. A cost function is then minimized to produce the new iterative learning control law design. Finally, a simulation based case study is given to illustrate the performance of the new design.
Keywords: Iterative learning control; Modified Newton method; Discrete nonlinear systems; Constrained optimization

Weixin Han, Harry L. Trentelman, Zhenhua Wang, Yi Shen,
Towards a minimal order distributed observer for linear systems,
Systems & Control Letters,
Volume 114,
2018,
Pages 59-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.011.
(http://www.sciencedirect.com/science/article/pii/S0167691118300409)
Abstract: In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only part of the output of the observed system, but also receives information on the state estimates of its neighbors.Each local observer should in this way generate an estimate of the plant state. In this paper we study the problem of existence of a reduced order distributed observer. We show that if the observed system is observable and the network graph is a strongly connected directed graph, then a distributed observer exists with state space dimension equal to Nn−∑i=1Npi, where N is the number of network nodes, n is the state space dimension of the observed plant, and pi is the rank of the output matrix of the observed output received by the ith local observer. In the case of a single observer, this result specializes to the well-known minimal order observer in classical observer design.
Keywords: Distributed estimation; Linear system observers; Minimal order; LMI’s; Sensor networks

Guangming Zhuang, Qian Ma, Baoyong Zhang, Shengyuan Xu, Jianwei Xia,
Admissibility and stabilization of stochastic singular Markovian jump systems with time delays,
Systems & Control Letters,
Volume 114,
2018,
Pages 1-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118300252)
Abstract: This paper deals with the admissibility analysis and stabilization of stochastic singular Markovian jump systems (SSMJSs) with time delays. More general conditions for the existence and uniqueness of the impulse-free solution to delayed SSMJSs are presented. Consequently, by constructing stochastic Lyapunov–Krasovskii functional and applying generalized Itô formula, new sufficient conditions for the stability of SSMJSs and delayed SSMJSs are obtained in terms of strict linear matrix inequalities. State feedback controller is designed to ensure stabilization of the delayed SSMJSs. Three illustrative examples, including an RLC circuit network and an oil catalytic cracking process, are employed to verify the effectiveness and usefulness of the obtained results.
Keywords: Stochastic singular systems; Markovian jump systems; Time-delay systems; Stochastic admissibility; State feedback control

Zehor Belkhatir, Taous Meriem Laleg-Kirati,
Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems,
Systems & Control Letters,
Volume 115,
2018,
Pages 26-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118300410)
Abstract: This paper proposes a two steps algorithm for the joint estimation of parameters and fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. A potential application of the proposed algorithm consists in estimating the fractional differentiation orders of a fractional neurovascular model along with the neural activity considered as an input for this model. To assess the performance of the proposed method, different numerical tests are conducted.
Keywords: Linear fractional order systems; Non-commensurate orders; Parameters and fractional differentiation orders estimation; Modulating functions method

Yusheng Wei, Zongli Lin,
Stability criteria of linear systems with multiple input delays under truncated predictor feedback,
Systems & Control Letters,
Volume 111,
2018,
Pages 9-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117302001)
Abstract: The model reduction technique as a feedback design approach for linear systems with input delays achieves finite spectrum assignment of the closed-loop system in a delay free form. The resulting predictor-type feedback law contains a distributed term that involves the convolution between the past input and the state transition matrix and hence causes difficulty in its implementation. For the purpose of easy implementation, the truncated predictor feedback (TPF) simplifies the predictor feedback by discarding the distributed term, and delay independent truncated predictor feedback further eliminates the delay-dependent exponential factor. In this paper, we consider the stabilization of a general linear system with multiple time-varying input delays by TPF or delay independent TPF. Stability criteria expressed in terms of input delays and the feedback parameter are derived through Lyapunov–Krasovskii stability analysis, and then numerically studied under both feedback laws.
Keywords: Multiple input delays; Stabilization; Truncated predictor feedback

Jianhui Huang, Xun Li, Tianxiao Wang,
Characterizations of closed-loop equilibrium solutions for dynamic mean–variance optimization problems,
Systems & Control Letters,
Volume 110,
2017,
Pages 15-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301792)
Abstract: Herein, we study the dynamic mean–variance portfolio optimization problems with deterministic coefficients. An intrinsic characterization of closed-loop equilibrium solutions is obtained for the first time. Our approach proposed here not only essentially differs from that in existing literature, but also avoids conventional complicated convergence arguments. Applying the characterization obtained, we prove that this optimization problem actually admits unique closed-loop equilibrium solution.
Keywords: Stochastic linear quadratic problems; Time-inconsistency; Dynamic mean–variance portfolio optimization; Closed-loop equilibrium solutions

Iasson Karafyllis, Miroslav Krstic,
Sampled-data boundary feedback control of 1-D linear transport PDEs with non-local terms,
Systems & Control Letters,
Volume 107,
2017,
Pages 68-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117301275)
Abstract: The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D inhomogeneous, linear, transport partial differential equations on bounded domains with constant velocity and non-local terms. It is shown that the emulation design based on the recently proposed continuous-time, boundary feedback, designed by means of backstepping, guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. It is also shown that, contrary to the parabolic case, a smaller sampling period implies a faster convergence rate with no upper bound for the achieved convergence rate. The obtained results provide stability estimates for the sup-norm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.
Keywords: Sampled-data control; Hyperbolic PDEs; Transport PDEs; Boundary feedback

Beata Sikora, Jerzy Klamka,
Constrained controllability of fractional linear systems with delays in control,
Systems & Control Letters,
Volume 106,
2017,
Pages 9-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.013.
(http://www.sciencedirect.com/science/article/pii/S0167691117301032)
Abstract: The paper presents finite-dimensional dynamical control systems described by linear fractional-order state equations with multiple delays in control. The constrained controls are considered. The set of admissible control values is assumed to be a compact set containing 0, a convex and compact set containing 0 in its interior, a cone with vertex at zero and a nonempty interior, or a convex and close cone with nonempty interior and vertex at zero. The definitions of various types of constrained controllability of the linear fractional systems with delays in control are formulated. New necessary and sufficient conditions for constrained relative controllability of fractional-order control systems with delayed controls are established and proved. Numerical examples are provided to illustrate the obtained theoretical results.
Keywords: Fractional systems; Linear control systems; Constrained controllability; Delays in control; Pseudo-transition matrix; The Caputo derivative

Annika Eichler, Herbert Werner,
Optimal convergence speed of consensus under constrained damping for multi-agent systems with discrete-time double-integrator dynamics,
Systems & Control Letters,
Volume 108,
2017,
Pages 48-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117301433)
Abstract: This paper considers the optimization of the convergence speed of consensus under given damping constraints for multi-agent systems with discrete-time double-integrator dynamics with fixed interconnection topology. This work summarizes and details existing results in the case of undirected topologies and extends them to directed ones. The interconnection topology is assumed to be connected or to contain a rooted-out branching, respectively. Depending on the minimum required damping, for undirected interconnection topologies in most cases analytic solutions are provided. The structure of these solutions is independent of the size of the network and only depends on the largest and second smallest eigenvalue of the corresponding Laplacian. For the remaining cases without analytic solutions provided, a combined bisection grid search is presented that solves the constrained optimization problem efficiently. This algorithm can also be applied to directed interconnection topologies and, as for the undirected case, converges to the single optimum. Simulation results are provided that demonstrate the effectiveness of the proposed approach.
Keywords: Multi-agent systems; Consensus problem; Consensus speed; Damping; Discrete-time systems; Double-integrator dynamics; Graph Laplacians

Jiapeng Xu, Chenglin Wen, Quanbo Ge, Daxing Xu,
Optimal multiple-sensor scheduling for general scalar Gauss–Markov systems with the terminal error,
Systems & Control Letters,
Volume 108,
2017,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.013.
(http://www.sciencedirect.com/science/article/pii/S016769111730138X)
Abstract: In this work, we study finite-horizon multiple-sensor scheduling for general scalar Gauss–Markov systems, extending previous results where only a class of systems are considered. The scheduling objective is to minimize the terminal estimation error covariance. At each time instant, only one sensor can transmit its measurement and each sensor has limited energy. Through building a comparison function and solving its monotone intervals, an efficient algorithm is designed to construct the optimal schedule. In addition, we also provide the result for selecting multiple sensors per time instant under an assumption. Examples are provided to illustrate the proposed results.
Keywords: Kalman filtering; Multiple-sensor scheduling; Terminal estimation error covariance; State estimation

Rafal Goebel,
Stability and robustness for saddle-point dynamics through monotone mappings,
Systems & Control Letters,
Volume 108,
2017,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.014.
(http://www.sciencedirect.com/science/article/pii/S0167691117301391)
Abstract: Motivated by recent interest in saddle-point dynamics, where, given a convex in x and concave in y function, trajectories follow the steepest descent in x and the steepest ascent in y, and where convergence of trajectories to saddle points is desired, this note revisits the maximal monotone mapping approach to saddle-point dynamics, mildly improves one convergence result, and proposes new results on the robustness of pointwise asymptotic stability of the set of saddle points. The results apply to nonsmooth convex/concave functions and constraints, and – as a special case – to projected saddle-point dynamics.
Keywords: Saddle-point dynamics; Monotone mappings; Convex–concave functions; Pointwise asymptotic stability; Robustness

C. Altafini,
Involutive flows and discretization errors for nonlinear driftless control systems,
Systems & Control Letters,
Volume 110,
2017,
Pages 29-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117301822)
Abstract: In a continuous-time nonlinear driftless control system, an involutive flow is a composition of input profiles that does not excite any Lie bracket. Such flow composition is trivial, as it corresponds to a “forth and back” cyclic motion obtained rewinding the system along the same path. The aim of this paper is to show that, on the contrary, when a (nonexact) discretization of the nonlinear driftless control system is steered along the same trivial input path, it produces a net motion, which is related to the gap between the discretization used and the exact discretization given by a Taylor expansion. These violations of involutivity can be used to provide an estimate of the local truncation error of numerical integration schemes. In the special case in which the state of the driftless control system admits a splitting into shape and phase variables, our result corresponds to saying that the geometric phases of the discretization need not obey an area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases.
Keywords: Discrete-time nonlinear control systems; Nonintegrability condition; Discretization; Lie brackets; Geometric phase; Geometric numerical integration; Local error computation

Mireille E. Broucke, Melkior Ornik, Abdol-Reza Mansouri,
A topological obstruction in a control problem,
Systems & Control Letters,
Volume 108,
2017,
Pages 71-79,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117301548)
Abstract: One of the important discoveries in control theory is a topological obstruction to continuous feedback stabilization for general nonlinear control systems. In this note we describe another topological obstruction arising from a very different control problem called the reach control problem. Motivated by a classical topological obstruction for extending continuous maps on spheres, we introduce the problem of extending continuous maps on simplices. It is shown that the same condition as in the sphere case gives rise to the obstruction.
Keywords: Reach control problem; Topological obstruction; Extension problem

Suhail M. Shah, Vivek S. Borkar,
Q-learning for Markov decision processes with a satisfiability criterion,
Systems & Control Letters,
Volume 113,
2018,
Pages 45-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300045)
Abstract: A reinforcement learning algorithm is proposed in order to solve a multi-criterion Markov decision process, i.e., an MDP with a vector running cost. Specifically, it combines a Q-learning scheme for a weighted linear combination of the prescribed running costs with an incremental version of replicator dynamics that updates the weights. The objective is that the time averaged vector cost meets prescribed asymptotic bounds. Under mild assumptions, it is shown that the scheme achieves the desired objective.
Keywords: Markov decision processes; Satisfiability; Q-learning; Replicator dynamics; Differential inclusions

Luca Consolini, Marco Locatelli, Andrea Minari, Aurelio Piazzi,
Corrigendum to “An optimal complexity algorithm for minimum-time velocity planning” [Systems & Control Letters 103 (2017) 50–57],
Systems & Control Letters,
Volume 108,
2017,
Page 80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117301706)

Mattia Mattioni, Salvatore Monaco, Dorothée Normand-Cyrot,
Nonlinear discrete-time systems with delayed control: A reduction,
Systems & Control Letters,
Volume 114,
2018,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300288)
Abstract: In this work, the notion of reduction is introduced for discrete-time nonlinear input-delayed systems. The retarded dynamics is reduced to a new system which is free of delays and equivalent (in terms of stabilizability) to the original one. Different stabilizing strategies are proposed over the reduced model. Connections with existing predictor-based methods are discussed. The methodology is also worked out over particular classes of time-delay systems as sampled-data dynamics affected by an entire input delay.
Keywords: Discrete-time systems; Nonlinear systems; Time-delay systems

M.V. Kulikova,
Square-root algorithms for maximum correntropy estimation of linear discrete-time systems in presence of non-Gaussian noise,
Systems & Control Letters,
Volume 108,
2017,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.016.
(http://www.sciencedirect.com/science/article/pii/S016769111730141X)
Abstract: Recent developments in the realm of state estimation of stochastic dynamic systems in the presence of non-Gaussian noise have induced a new methodology called the maximum correntropy filtering. The filters designed under the maximum correntropy criterion (MCC) utilize a similarity measure (or correntropy) between two random variables as a cost function. They are shown to improve the estimators’ robustness against outliers or impulsive noises. In this paper we explore the numerical stability of linear filtering technique proposed recently under the MCC approach. The resulted estimator is called the maximum correntropy criterion Kalman filter (MCC-KF). The purpose of this study is two-fold. First, the previously derived MCC-KF equations are revised and the related Kalman-like equality conditions are proved. Based on this theoretical finding, we improve the MCC-KF technique in the sense that the new method possesses a better estimation quality with the reduced computational cost compared with the previously proposed MCC-KF variant. Second, we devise some square-root implementations for the newly-designed improved estimator. The square-root algorithms are well known to be inherently more stable than the conventional Kalman-like implementations, which process the full error covariance matrix in each iteration step of the filter. Additionally, following the latest achievements in the KF community, all square-root algorithms are formulated here in the so-called array form. It implies the use of orthogonal transformations for recursive update of the required filtering quantities and, thereby, no loss of accuracy is incurred. Apart from the numerical stability benefits, the array form also makes the modern Kalman-like filters better suited to parallel implementation and to very large scale integration (VLSI) implementation. All the MCC-KF variants developed in this paper are demonstrated to outperform the previously proposed MCC-KF version in two numerical examples.
Keywords: Maximum correntropy criterion; Kalman filter; Square-root filtering; Robust estimation

Chong Lin, Bing Chen, Peng Shi, Jin-Peng Yu,
Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems,
Systems & Control Letters,
Volume 112,
2018,
Pages 31-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117302232)
Abstract: This paper is concerned with observer-based stabilization for fractional-order descriptor systems with order 1≤α<2. A necessary and sufficient condition is proposed for the control design by using appropriate matrix variable decoupling technique. The developed results are more general and useful than some existing works, and cover them as special cases, in which only sufficient conditions were presented, in particular, for normal fractional-order systems. Illustrative examples are provided to verify and demonstrate the effectiveness and potential of the theoretic results obtained.
Keywords: Fractional-order systems; Descriptor systems; Admissibility; Stabilization; Observer-based control

T. Ahmed-Ali, F. Giri, M. Krstic, M. Kahelras,
PDE based observer design for nonlinear systems with large output delay,
Systems & Control Letters,
Volume 113,
2018,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.001.
(http://www.sciencedirect.com/science/article/pii/S016769111830001X)
Abstract: In this paper, we develop a new observer design method for nonlinear systems with large transport delays. The new observer design is a generalization of the PDE-based backstepping-like observer design approach. First developed for delayed linear systems, this approach relies on a modelling of the output time-delay by a 1st order hyperbolic equation, leading to an ODE–PDE representation of the system, and on coordinate transformations of the innovative system. The major technical challenge, that is faced in the generalization of the approach to nonlinear systems, consists in making it applicable in the case of an arbitrarily large time-delay D. This issue is presently coped with by redesigning the cascade observer method to fit ODE–PDE systems. A new class of observers is thus obtained involving a set of cascaded high-gain state observers and output predictors. The latter are defined by PDEs that provide estimates of the system future outputs y(t+x) for all x∈[0,D]. The exponential stability of the observer is proved using a set of Lyapunov functionals and its performances are illustrated by simulation.
Keywords: Delay systems; Nonlinear systems; Transport PDEs; Observer design

Corrado Possieri, Andrew R. Teel,
A Lyapunov theorem certifying global weak reachability for stochastic difference inclusions with random inputs,
Systems & Control Letters,
Volume 109,
2017,
Pages 37-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301780)
Abstract: In this paper, a Lyapunov condition certifying global weak reachability of a compact set is given for stochastic, set–valued, discrete-time systems. With respect to such systems, under mild regularity assumptions, it is shown that the existence of a lower semicontinuous function that decreases in expected value for at least one measurable selection from the set-valued mapping outside a compact set is a sufficient condition for global weak reachability of such a set.

Junfeng Wu, Yuzhe Li, Daniel E. Quevedo, Ling Shi,
Improved results on transmission power control for remote state estimation,
Systems & Control Letters,
Volume 107,
2017,
Pages 44-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301263)
Abstract: We consider a sensor transmission power control problem for remote state estimation. In this problem, a sensor sends its local estimate to a remote estimator over a wireless packet-dropping communication channel. The transmission power is determined by a recently proposed algorithm which uses the innovative information contained in the measurement. In the current paper, we focus on parameter optimization arising from the selection of design parameters for this power controller. The existing work obtained a suboptimal solution to the parameter optimization problem, while by using a vector rearrangement inequality argument and the vector majorization, we now show that there exists an optimal solution within a subset of the whole feasible set. By leveraging this property, we obtain an optimal solution via solving a convex optimization problem.
Keywords: Kalman filtering; Transmission power control; Packet loss; Majorization; Convex optimization

Shengquan Xiang,
Small-time local stabilization for a Korteweg–de Vries equation,
Systems & Control Letters,
Volume 111,
2018,
Pages 64-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.11.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117302116)
Abstract: This paper focuses on the (local) small-time stabilization of a Korteweg–de Vries equation on bounded interval, thanks to a time-varying Dirichlet feedback law on the left boundary. Recently, backstepping approach has been successfully used to prove the null controllability of the corresponding linearized system, instead of Carleman inequalities. We use the “adding an integrator” technique to gain regularity on boundary control term which clears the difficulty from getting stabilization in small time.
Keywords: Korteweg–de Vries; Backstepping; Small-time stabilization; Adding an integrator

Dany Abou Jaoude, Mazen Farhood,
Distributed control of nonstationary LPV systems over arbitrary graphs,
Systems & Control Letters,
Volume 108,
2017,
Pages 23-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.017.
(http://www.sciencedirect.com/science/article/pii/S0167691117301421)
Abstract: This paper deals with the ℓ2-induced norm control of discrete-time, nonstationary linear parameter-varying (NSLPV) subsystems, represented in a linear fractional transformation (LFT) framework and interconnected over arbitrary directed graphs. Communication between the subsystems is subjected to a one-step time-delay. NSLPV models have state-space matrix-valued functions with explicit dependence on time-varying terms that are known a priori, as well as parameters that are not known a priori but are available for measurement at each discrete time-step. The sought controller has the same interconnection and LFT structures as the plant. Convex analysis and synthesis results are derived using a parameter-independent Lyapunov function. These conditions are infinite dimensional in general, but become finite dimensional in the case of eventually time-periodic subsystems interconnected over finite graphs. The method is applied to an illustrative example.
Keywords: Nonstationary linear parameter-varying (NSLPV) systems; Distributed control; Arbitrary graphs; Communication latency; Eventually time-periodic systems


Editorial Board,
Systems & Control Letters,
Volume 111,
2018,
Page ii,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30219-0.
(http://www.sciencedirect.com/science/article/pii/S0167691117302190)

Daniel Silvestre, Paulo Rosa, João P. Hespanha, Carlos Silvestre,
Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach,
Systems & Control Letters,
Volume 106,
2017,
Pages 32-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301019)
Abstract: This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.
Keywords: Fault detection; Linear parameter-varying; Coprime factorization; Deadbeat observers

Jorge R. Chávez-Fuentes, Jorge E. Mayta, Eduardo F. Costa, Marco H. Terra,
Stochastic and exponential stability of discrete-time Markov jump linear singular systems,
Systems & Control Letters,
Volume 107,
2017,
Pages 92-99,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.006.
(http://www.sciencedirect.com/science/article/pii/S016769111730124X)
Abstract: In this paper stochastic and almost sure stability of a Markov jump linear singular system are analyzed. First, it is given a set of coupled generalized Lyapunov equations to characterize the stochastic stability of the system. Second, it is introduced a top Lyapunov exponent to give a sufficient condition for almost sure stability. Our approach captures the solvability issue arising in this class of systems, leading to Lyapunov equations whose parameters reflex the solvability in an explicit manner. Two examples are presented in order to show the effectiveness of the proposed stability analysis.
Keywords: Stability; Markovian jump linear systems; Lyapunov exponent; Lyapunov equations; Singular systems

Vakhtang Lomadze,
Converting high order linear PDEs to first order: Noncommutative case,
Systems & Control Letters,
Volume 109,
2017,
Pages 49-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301810)
Abstract: A straightforward way is offered to convert a system of high order linear functional equations of various type into a system of first order equations.
Keywords: Ore algebra; Tensor product; Exact sequence; Jordan pencil

Dan Pilbauer, Wim Michiels, Jaroslav Bušek, David Osta, Tomáš Vyhlídal,
Control design and experimental validation for flexible multi-body systems pre-compensated by inverse shapers,
Systems & Control Letters,
Volume 113,
2018,
Pages 93-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691118300033)
Abstract: A complex methodology for control of flexible multi-body systems is proposed with the objective to achieve a favorable distribution of system motion so that the oscillatory mode of the flexible part is not excited. As the key element, the recently proposed concept of a feedback loop with an inverse distributed delay shaper is adopted. Unlike in existing works, the mutual coupling between the primary (controlled) structure and secondary (flexible) structure of oscillatory nature is explicitly taken into account in the controller design. First, an easy to apply method to isolate the flexible mode to be targeted in the shaper design is proposed. Secondly, the interconnection of the system, shaper and the controller is formulated as a set of delay differential algebraic equations. Then the spectral optimization control design technique is applied to achieve fast dynamics of the infinite dimensional system. The viability of the overall methodology is validated by both simulations and experiments in an extensive case study example.
Keywords: Time-delay; Inverse shapers; Vibration control; Spectral optimization; Spectral abscissa


Editorial Board,
Systems & Control Letters,
Volume 109,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30193-7.
(http://www.sciencedirect.com/science/article/pii/S0167691117301937)

Ya-Jun Pan, Herbert Werner, Zipeng Huang, Marcus Bartels,
Distributed cooperative control of leader–follower multi-agent systems under packet dropouts for quadcopters,
Systems & Control Letters,
Volume 106,
2017,
Pages 47-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117301056)
Abstract: This paper is to develop a novel distributed leader–follower algorithm for multi-agent systems in the event of stochastic communication link failure over the network. Bernoulli distribution is applied to represent the data dropout during operation while the data dropout properties of each communication links are independent from each other. Sufficient conditions for a stabilizing controller design are developed by using Lyapunov-based methodologies and Linear Matrix Inequality (LMIs) techniques. The stability condition is then decomposed into small robust stability conditions with the size of a single agent, provided that the interaction topology of the followers is an undirected graph, which leads to efficient solutions even in case that the number of agents is large and a high order system dynamics of the agent is considered. The main result is to ensure the mean square exponential stability of the overall system reaching consensus. The case of consecutive data losses in any of the communication links is also discussed in the same framework. Leader-following numerical simulations with a group of agents including quadcopters are successfully conducted to demonstrate the effectiveness of the novel consensus algorithm in this paper. The results show that the consensus achievement is incorporating the data loss probability; however a higher data loss rate may cause a longer time for agents to achieve consensus.
Keywords: Multi-agent systems; Cooperative control; Decomposition; Packet dropouts; Lyapunov function; Quadcopters

Junmin Peng, Chaoyong Li, Xudong Ye,
Cooperative control of high-order nonlinear systems with unknown control directions,
Systems & Control Letters,
Volume 113,
2018,
Pages 101-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.014.
(http://www.sciencedirect.com/science/article/pii/S0167691118300215)
Abstract: In this paper, we investigate output synchronization problem of nonlinear systems that can be transformed into strict feedback form with unknown control direction. To this end, an augmented Laplacian potential function is introduced to construct local level distributed adaptive controllers such that outputs of networked agents can be synchronized while all other states maintain bounded. Moreover, tuning functions are designed to reduce the order of the parameter updater. In contrast to conventional adaptive backstepping procedure, both the parameter updating law and tuning function of the proposed scheme take advantage of information flow among networked agents and thus distributive in nature. It is proved that output synchronization of the entire network can be achieved by properly choosing Nussbaum functions, provided the information graph is undirected and connected. Furthermore, we also proposed a way to define a proper Nussbaum function. Simulation results are presented to verify the effectiveness of the proposed schemes.
Keywords: Synchronization; Nussbaum; Adaptive control; Strict feedback

Fang Shang, Yungang Liu, Chengdong Li,
Global stabilization for feedforward nonlinear systems with unknown control direction and unknown growth rate,
Systems & Control Letters,
Volume 111,
2018,
Pages 58-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.11.005.
(http://www.sciencedirect.com/science/article/pii/S016769111730213X)
Abstract: This paper investigates the global adaptive state feedback controller design for a class of feedforward nonlinear systems with completely unknown control direction and unknown growth rate. Since the control direction, i.e., the sign of the control coefficient, is unknown, the control problem becomes much more challenging, to which a Nussbaum-type function is exploited. Moreover, the systems heavily depend on the unmeasured states with unknown growth rate, and hence a dynamic gain, rather than a constant one, is adopted to compensate the large system unknowns. For control design, a suitable state transformation is first introduced for the original system. Then, the state feedback controller is proposed based on an appropriate Nussbaum-type function and a dynamic high gain. It is shown that the state of the original system converges to zero, while the other states of the closed-loop system are globally bounded. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.
Keywords: Feedforward nonlinear systems; Unknown control direction; Unknown growth rate; Global stabilization; Adaptive control

Xuefang Li, Dong Shen,
Two novel iterative learning control schemes for systems with randomly varying trial lengths,
Systems & Control Letters,
Volume 107,
2017,
Pages 9-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117301214)
Abstract: This paper proposes two novel improved iterative learning control (ILC) schemes for systems with randomly varying trial lengths. Different from the existing works on ILC with variable trial lengths that advocate to replace the missing control information by zero, the proposed learning algorithms are equipped with a searching mechanism to collect useful but avoid redundant past tracking information, which could expedite the learning speed. The searching mechanism is realized by the newly defined stochastic variables and an iteratively-moving-average operator. The convergence of the proposed learning schemes is strictly proved based on the contraction mapping methodology. Two illustrative examples are provided to show the superiorities of the proposed approaches.
Keywords: Iterative learning control; Learning convergence; Randomly varying trial length

Hideki Sano,
Stability analysis of the telegrapher’s equations with dynamic boundary condition,
Systems & Control Letters,
Volume 111,
2018,
Pages 34-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.11.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117302025)
Abstract: This paper is concerned with the stability analysis of a distributed parameter circuit with dynamic boundary condition. The distributed parameter circuit is written by the telegrapher’s equations whose boundary condition is described by an ordinary differential equation. First of all, it is shown that, for any physical parameters of the circuit, the system operator generates an exponentially stableC0-semigroup on a Hilbert space. However, it is not clear whether the decay rate of the semigroup is the most precise one. In this paper, the spectral analysis is conducted for the system satisfying the distortionless condition, and it is shown that the semigroup satisfies the spectrum determined growthcondition.
Keywords: Distributed parameter circuit; Dynamic boundary condition; Semigroup; Spectrum determined growth condition

Qinghua Zhang,
On stability of the Kalman filter for discrete time output error systems,
Systems & Control Letters,
Volume 107,
2017,
Pages 84-91,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.011.
(http://www.sciencedirect.com/science/article/pii/S0167691117301299)
Abstract: The stability of the Kalman filter is classically ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. This paper studies the case of discrete time output error (OE) systems, in which the process noise is totally absent. The classical stability analysis assuming the controllability regarding the process noise is thus not applicable. It is shown in this paper that the uniform complete observability is sufficient to ensure the stability of the Kalman filter applied to time varying OE systems, regardless of the stability of the OE systems. Though the continuous time case has been studied recently, the results on continuous time systems cannot be directly transposed to discrete time systems, because of a difficulty related to the observability of the discrete time filter error dynamics system.
Keywords: Kalman filter; Discrete time output error system; Time varying system; Stability

Delphine Bresch-Pietri, Christophe Prieur, Emmanuel Trélat,
New formulation of predictors for finite-dimensional linear control systems with input delay,
Systems & Control Letters,
Volume 113,
2018,
Pages 9-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117302268)
Abstract: This paper focuses on a prediction-based control for linear time invariant systems subject to a constant input delay, also known as the Artstein reduction approach. Standardly, this method consists in considering a predicted delay-free system, on which one can design straightforwardly a stabilizing controller. The resulting controller is then defined through an implicit integral equation, involving both the original system state and past values of the input. We propose here an alternative formulation which allows to write explicitly the Artstein transformation, and thus the corresponding controller, in terms of past values of the state only. This formal explicit formulation is the main contribution of the paper.
Keywords: Time-delay systems; Finite spectrum assignment; Prediction-based controllers

Xiaodi Li, Yanhui Ding,
Razumikhin-type theorems for time-delay systems with Persistent impulses,
Systems & Control Letters,
Volume 107,
2017,
Pages 22-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301172)
Abstract: The main results of the paper are generalizations of the Razumikhin classical theorems for stability analysis of impulsive time-delay systems. By employing Lyapunov–Razumikhin method and impulsive control theory, several Razumikhin-type theorems for uniform stability and global exponential stability are obtained. The significance and novelty of the results lie in that the criteria for stability of impulsive time-delay systems admit the existence of persistent impulses and unbounded time-varying delays. Two examples are provided to show the effectiveness of the proposed results.
Keywords: Time-delay systems; Persistent impulse; Unbounded time-varying delays; Stability; Lyapunov–Razumikhin method

Yifen Mu,
Stackelberg–Nash equilibrium, social welfare and optimal structure in hierarchical continuous Public Goods game,
Systems & Control Letters,
Volume 112,
2018,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117302141)
Abstract: This paper studies Stackelberg–Nash equilibrium, social welfare and optimal structure of hierarchical Public Goods game in which the players have continuous action spaces. There can be multiple leaders, followers or levels and the leaders are assumed to take linear strategies with respect to the followers’ actions. Explicit forms of Stackelberg–Nash equilibriums of the game under different structures are solved from which social welfare index emerges with good properties. Based on these the optimal 2-level structure for any given population is proved and constructed in steps less than the population size. Moreover, equilibrium under the simplest three-level structure is computed, which implies a bound of hierarchy for theoretical analysis. Results in this paper are rigorous and show interesting phenomena in hierarchical games, which may help decision-making in practice especially in hierarchical systems.
Keywords: Hierarchical games; Stackelberg–Nash equilibrium; Public goods game; Social welfare; Optimal structure

Henrik Anfinsen, Ole Morten Aamo,
Model reference adaptive control of n+1 coupled linear hyperbolic PDEs,
Systems & Control Letters,
Volume 109,
2017,
Pages 1-11,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.006.
(http://www.sciencedirect.com/science/article/pii/S016769111730155X)
Abstract: We solve a model reference adaptive control (MRAC) problem for a class of systems consisting of n+1 coupled linear hyperbolic partial differential equations. The goal is achieved from a single boundary sensing anti-collocated with the actuation, with the only knowledge of the system being the system’s transport delays and the sign of the product of the actuation and measurement scaling constants. Boundedness in L2 is shown for all signals in the closed loop system. Moreover, the adaptive output feedback stabilization problem is a subproblem of the MRAC problem, and it is shown that if the reference signal is set identically zero, the system’s L2-norms are bounded and square integrable. The theory is demonstrated in simulations.
Keywords: Distributed systems; Adaptive control; Backstepping

Mohammed Safi, Lucie Baudouin, Alexandre Seuret,
Tractable sufficient stability conditions for a system coupling linear transport and differential equations,
Systems & Control Letters,
Volume 110,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117301603)
Abstract: This paper deals with the stability analysis of a system of finite dimension coupled to a vectorial transport equation. We develop here a new method to study the stability of such a system, coupling ordinary and partial differential equations, using linear matrix inequalities led by the choice of an appropriate Lyapunov functional. To this end, we exploit Legendre polynomials and their properties, and use a Bessel inequality to measure the contribution of our approximation. The exponential stability of a wide class of delay systems is a direct consequence of this study, but above all, we are detailing here a new approach in the consideration of systems coupling infinite and finite dimensional dynamics. The coupling with a vectorial transport equation is a first step that already prove the interest of the method, bringing hierarchized conditions for stability. We will give exponential stability results and their proofs. Our approach will finally be tested on several academic examples.
Keywords: Transport equation; Lyapunov stability; Bessel inequality

Christoph Kawan,
Exponential state estimation, entropy and Lyapunov exponents,
Systems & Control Letters,
Volume 113,
2018,
Pages 78-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.011.
(http://www.sciencedirect.com/science/article/pii/S0167691118300185)
Abstract: In this paper we study the notion of estimation entropy established by Liberzon and Mitra. This quantity measures the smallest rate of information about the state of a system above which an exponential state estimation with a given exponent is possible. We show that this concept is closely related to the α-entropy introduced by Thieullen and we give a lower estimate in terms of Lyapunov exponents, assuming that the system preserves a volume measure, which includes all Hamiltonian and symplectic systems. Although in its current form mainly interesting from a theoretical point of view, our result could be a first step towards a more practical analysis of state estimation under communication constraints.
Keywords: Minimal data rates; Estimation entropy; 
               α-entropy; Lyapunov exponents; Volume-preserving systems

Cristopher Hermosilla, Richard Vinter, Hasnaa Zidani,
Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints,
Systems & Control Letters,
Volume 109,
2017,
Pages 30-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117301688)
Abstract: This work aims at studying some optimal control problems with convex state constraint sets. It is known that for state constrained problems, and when the state constraint set coincides with the closure of its interior, the value function satisfies a Hamilton–Jacobi equation in the constrained viscosity sense. This notion of solution has been introduced by H.M. Soner (1986) and provides a characterization of the value functions in many situations where an inward pointing condition (IPC) is satisfied. Here, we first identify a class of control problems where the constrained viscosity notion is still suitable to characterize the value function without requiring the IPC. Moreover, we generalize the notion of constrained viscosity solutions to some situations where the state constraint set has an empty interior.
Keywords: State constraint sets; Optimal control problems; Convex constraints; HJB equations; Viscosity solutions

György Lipták, Katalin M. Hangos, Mihály Pituk, Gábor Szederkényi,
Semistability of complex balanced kinetic systems with arbitrary time delays,
Systems & Control Letters,
Volume 114,
2018,
Pages 38-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.008.
(http://www.sciencedirect.com/science/article/pii/S016769111830029X)
Abstract: In this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems. We prove the uniqueness of equilibrium solutions within the time delayed positive stoichiometric compatibility classes for such models. In our main result we prove the semistability of the equilibrium solutions for complex balanced systems with arbitrary time delays using an appropriate Lyapunov–Krasovskii functional and LaSalle’s invariance principle. As a consequence, we obtain that every positive complex balanced equilibrium solution is locally asymptotically stable relative to its positive stoichiometric compatibility class.
Keywords: Nonnegative systems; Kinetic systems; Chemical reaction networks; Stability theory; Time delay; Logarithmic Lyapunov–Krasovskii functionals

Fu Lin,
Performance of leader–follower multi-agent systems in directed networks,
Systems & Control Letters,
Volume 113,
2018,
Pages 52-58,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.009.
(http://www.sciencedirect.com/science/article/pii/S0167691118300100)
Abstract: We consider leader–follower multi-agent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader–follower systems is quantified by the steady-state variance of the deviation of the followers from the desired trajectory. We study the asymptotic scaling of the variance in directed lattices in one, two, and three dimensions. We show that in 1D and 2D the variance of the followers’ deviation increases to infinity as one moves away from the leader, while in 3D the variance remains bounded regardless of the network size. We prove that the variance of the followers scales as a square-root function of the distance to the leader in 1D and a logarithmic function in 2D lattices.
Keywords: Consensus; Controller architecture; Directed networks; Leader–follower systems; Toeplitz matrices


Editorial Board,
Systems & Control Letters,
Volume 113,
2018,
Page ii,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(18)30034-3.
(http://www.sciencedirect.com/science/article/pii/S0167691118300343)

Wenxiao Zhao, Han-Fu Chen, Er-Wei Bai, Kang Li,
Local variable selection of nonlinear nonparametric systems by first order expansion,
Systems & Control Letters,
Volume 111,
2018,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117301846)
Abstract: Local variable selection by first order expansion for nonlinear nonparametric systems is investigated in the paper. By substantially modifying the algorithms developed in our earlier work (Bai et al., 2014), the previous results have been considerably strengthened under much less restrictive conditions. Firstly, the estimates generated by the modified algorithms are shown to have both the set and parameter convergence with probability one, rather than only the set convergence in probability given in our earlier work. Secondly, several technical assumptions, e.g., the lower and upper bounds on the growth of some random sequences, which practically are uncheckable, have been removed. Thirdly, not only the consistency but also the convergence rate of estimates have been established. Besides, a generalization of the proposed algorithms is also introduced.
Keywords: Nonlinear ARX system; Variable selection; Local linear estimator; Strong consistency

Ivan Polekhin,
On topological obstructions to global stabilization of an inverted pendulum,
Systems & Control Letters,
Volume 113,
2018,
Pages 31-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300069)
Abstract: We consider a classical problem of control of an inverted pendulum by means of a horizontal motion of its pivot point. We suppose that the control law can be non-autonomous and non-periodic w.r.t. the position of the pendulum. It is shown that global stabilization of the vertical upward position of the pendulum cannot be obtained for any Lipschitz control law, provided some natural assumptions. Moreover, we show that there always exists a solution separated from the vertical position and along which the pendulum never becomes horizontal. Hence, we also prove that global stabilization cannot be obtained in the system where the pendulum can impact the horizontal plane (for any mechanical model of impact). Similar results are presented for several analogous systems: a pendulum on a cart, a spherical pendulum, and a pendulum with an additional torque control.
Keywords: Stabilization of an inverted pendulum; Pendulum on a cart; Periodic solution; Topological obstructions to stabilization; Partial stability


Editorial Board,
Systems & Control Letters,
Volume 112,
2018,
Page ii,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(18)30015-X.
(http://www.sciencedirect.com/science/article/pii/S016769111830015X)

Dongsheng Du, Shengyuan Xu, Vincent Cocquempot,
Actuator fault estimation for discrete-time switched systems with finite-frequency,
Systems & Control Letters,
Volume 108,
2017,
Pages 64-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301561)
Abstract: This paper deals with the problem of actuator fault estimation observer design for discrete-time switched systems with finite-frequency. The frequencies of the fault and the unknown input disturbance are assumed to be in a finite range. A finite frequency fault estimation observer is proposed to estimate the actuator fault in the entire frequency domain. Based on the generalized Kalman–Yakubovic–Popov (KYP) lemma and the switched Lyapunov function method, the efficient conditions are obtained to achieve the fault estimation observer design. Finally, an example is given to illustrate the proposed technique.
Keywords: Fault estimation; Finite frequency; Discrete-time switched system

Atreyee Kundu, Debasish Chatterjee,
Stabilizing switching signals: A transition from point-wise to asymptotic conditions,
Systems & Control Letters,
Volume 106,
2017,
Pages 16-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117301044)
Abstract: Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an umbrella framework. We achieve this in two steps: Firstly, given a family of systems, possibly containing unstable dynamics, we propose a new and general class of stabilizing switching signals. Secondly, we demonstrate that prior results based on both point-wise and asymptotic characterizations follow our result. This is the first attempt in the switched systems literature where these switching signals are unified under one banner.
Keywords: Switched systems; Stabilizing switching signals; Asymptotic stability; Multiple Lyapunov functions

Yirmeyahu J. Kaminski, Jean Lévine, François Ollivier,
Intrinsic and apparent singularities in differentially flat systems, and application to global motion planning,
Systems & Control Letters,
Volume 113,
2018,
Pages 117-124,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.013.
(http://www.sciencedirect.com/science/article/pii/S0167691118300203)
Abstract: In this paper, we study the singularities of differentially flat systems, in the perspective of providing global or semi-global motion planning solutions for such systems: flat outputs may fail to be globally defined, thus potentially preventing from planning trajectories leaving their domain of definition, the complement of which we call singular. Such singular subsets are classified into two types: apparent and intrinsic. A rigorous definition of these singularities is introduced in terms of atlas and local charts in the framework of the differential geometry of jets of infinite order and Lie–Bäcklund isomorphisms. We then give an inclusion result allowing to effectively compute all or part of the intrinsic singularities. Finally, we show how our results apply to the global motion planning of the celebrated example of non holonomic car.
Keywords: Differential flatness; Jets of infinite order; Lie–Bäcklund isomorphism; Atlas; Local chart; Apparent and intrinsic singularity; Global motion planning

Bowen Yi, Romeo Ortega, Weidong Zhang,
Relaxing the conditions for parameter estimation-based observers of nonlinear systems via signal injection,
Systems & Control Letters,
Volume 111,
2018,
Pages 18-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.011.
(http://www.sciencedirect.com/science/article/pii/S0167691117302013)
Abstract: Parameter estimation-based observers are a new kind of state reconstruction methods where the state observation task is translated into an on-line parameter estimation problem. A key step for its application is the transformation of the system dynamics into a particular cascade form, which involves the solution of a partial differential equation that, moreover, should satisfy some injective requirement. In this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks. In this way, we make this observer applicable to a wider class of nonlinear systems—even with indistinguishable states. The application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems.
Keywords: Signal injection; Nonlinear systems; Observer; Parameter estimation

D. Bauso,
Consensus via multi-population robust mean-field games,
Systems & Control Letters,
Volume 107,
2017,
Pages 76-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117301287)
Abstract: In less prescriptive environments where individuals are told ‘what to do’ but not ‘how to do’, synchronization can be a byproduct of strategic thinking, prediction, and local interactions. We prove this in the context of multi-population robust mean-field games. The model sheds light on a multi-scale phenomenon involving fast synchronization within the same population and slow inter-cluster oscillation between different populations.
Keywords: Synchronization; Consensus; Mean-field games

Jung Hoon Kim, Tomomichi Hagiwara,
Upper/lower bounds of generalized H2 norms in sampled-data systems with convergence rate analysis and discretization viewpoint,
Systems & Control Letters,
Volume 107,
2017,
Pages 28-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301202)
Abstract: This paper considers linear time-invariant (LTI) sampled-data systems and studies their generalized H2 norms. They are defined as the induced norms from L2 to L∞, in which two types of the L∞ norm of the output are considered as the temporal supremum magnitude under the spatial ∞-norm and 2-norm. The input/output relation of sampled-data systems is first formulated under their lifting-based treatment. We then develop a method for computing the generalized H2 norms with operator-theoretic gridding approximation. This method leads to readily computable upper bounds as well as lower bounds of the generalized H2 norms, whose gaps tend to 0 at the rate of 1∕N with the gridding approximation parameter N. An approximately equivalent discretization method of the generalized plant is further provided as a fundamental step to addressing the controller synthesis problem of minimizing the generalized H2 norms of sampled-data systems. Finally, a numerical example is given to show the effectiveness of the computation method.
Keywords: Sampled-data systems; 
               L∞∕L2-induced norm; Discretization; Gridding; Operator-theoretic approach

Mohamadreza Ahmadi, Giorgio Valmorbida, Antonis Papachristodoulou,
Safety verification for distributed parameter systems using barrier functionals,
Systems & Control Letters,
Volume 108,
2017,
Pages 33-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117301445)
Abstract: We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (integral) inequalities, then the solutions of the system do not enter the unsafe set. Therefore, the proposed method does not require finite-dimensional approximations of the distributed parameter system. Furthermore, for PDEs with polynomial data, we solve the associated integral inequalities using semi-definite programming (SDP) based on a method that relies on a quadratic representation of the integrands of integral inequalities. The proposed method is illustrated through examples.
Keywords: Safety verification; Barrier certificates; Sum-of-Squares programming; Distributed parameter systems

V. Léchappé, E. Moulay, F. Plestan,
Prediction-based control of LTI systems with input and output time-varying delays,
Systems & Control Letters,
Volume 112,
2018,
Pages 24-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117302256)
Abstract: The stability of a prediction-based controller is studied in presence of time-varying delays both in the input and in the output. Thanks to the reduction method and a Lyapunov–Krasovskii analysis, stability conditions are derived. A comparison is also made between the single input delay and single output delay cases. It is shown that this method can be applied to stabilize output delay systems without restriction on the delay rate. The results are illustrated numerically on a double integrator.
Keywords: Prediction-based control; Input delay; Output delay; Time-varying delay; Reduction method

Guoquan Huang,
Towards consistent filtering for discrete-time partially-observable nonlinear systems,
Systems & Control Letters,
Volume 106,
2017,
Pages 87-95,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117301160)
Abstract: In this paper, we study the filter consistency of discrete-time nonlinear systems with partially-observable measurements, where the full state is not reconstructable from the available measurements at each time step. Linearized filters such as the extended Kalman filter (EKF) which are realized based on the corresponding linearized systems, may become inconsistent. Relying on a novel decomposition of the observability matrix based on different measurement sources, we show that the filter acquires spurious information from the measurements of each source, which erroneously reduces the uncertainty of the state estimates and hence causes inconsistency. Based on this key insight, we propose an information-aware methodology and develop two novel EKF algorithms of computing filter Jacobians which ensure that all decompositions of the observability matrix have nullspace of correct dimensions. In the first, the linearization points are selected so as to minimize their expected linearization errors under the constraints that the decompositions of the observability matrix have correct nullspace. In the second, we project the canonical measurement Jacobian onto the actual information-available directions. The proposed approaches are shown to significantly outperform the canonical EKF in the particular application of radar-based target tracking.
Keywords: Nonlinear filtering; Extended Kalman filter; Consistency; Fisher information matrix; Observability matrix; Nonlinear systems

M. Ouzahra,
Exponential stability of nondissipative linear system in Banach space and application to unbounded bilinear systems,
Systems & Control Letters,
Volume 109,
2017,
Pages 53-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117301834)
Abstract: We consider linear control systems of the form dz(t)dt=Az(t)−ρBz(t), where ρ is a real parameter, A is the infinitesimal generator of a linear C0-semigroup of contractions S0(t) on a Banach space X and the linear perturbation B is a relatively bounded operator with respect to A. We provide necessary and sufficient conditions for exponential stability of the above system. Our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators. Applications to hyperbolic like equations are considered.
Keywords: Relatively bounded operator; Uniform exponential stabilization; Linear semigroups; Bilinear systems


Editorial Board,
Systems & Control Letters,
Volume 106,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30131-7.
(http://www.sciencedirect.com/science/article/pii/S0167691117301317)

Qingkai Yang, Ming Cao, Hector Garcia de Marina, Hao Fang, Jie Chen,
Distributed formation tracking using local coordinate systems,
Systems & Control Letters,
Volume 111,
2018,
Pages 70-78,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.11.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117302128)
Abstract: This paper studies the formation tracking problem for multi-agent systems, for which a distributed estimator–controller scheme is designed relying only on the agents’ local coordinate systems such that the centroid of the controlled formation tracks a given trajectory. By introducing a gradient descent term into the estimator, the explicit knowledge of the bound of the agents’ speed is not necessary in contrast to existing works, and each agent is able to compute the centroid of the whole formation in finite time. Then, based on the centroid estimation, a distributed control algorithm is proposed to render the formation tracking and stabilization errors to converge to zero, respectively. Finally, numerical simulations are carried to validate our proposed framework for solving the formation tracking problem.
Keywords: Formation control; Cooperative control; Rigidity graph theory; Multi-agent systems

Mohammad Mahdi Share Pasand, Mohsen Montazeri,
Controllability and stabilizability of multi-rate sampled data systems,
Systems & Control Letters,
Volume 113,
2018,
Pages 27-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118300057)
Abstract: This paper gives sufficient conditions for controllability and stabilizability of multi-rate sampled data systems. For this purpose, it is firstly proposed that if the actuator communication sequence of a bandwidth limited networked system is equidistant, then the resulting model is mathematically equivalent to a multi-rate sampled data system. Secondly, recent results on controllability and stabilizability of bandwidth limited networked systems are reduced to the case of equidistant communication sequences. The established conditions enhance existing results on controllability and stabilizability of multi-rate sampled data systems. Also, it is shown that two independently established conditions for controllability and stabilizability of networked systems are equivalent in the special case of equidistant actuator communication sequences.
Keywords: Multi-rate systems; Networked control systems; Structural properties; Communication sequence characteristic polynomial

Hanbing Liu,
Impulse output feedback stabilization of Fisher’s equation,
Systems & Control Letters,
Volume 107,
2017,
Pages 17-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117301196)
Abstract: An explicit impulse output feedback controller has been designed in Phung (2016) for stabilization of the linear heat equation. The aim of this work is to show that the feedback controller of the same form as in Phung (2016) can locally exponentially stabilize the equilibrium solutions to Fisher’s equation in L2(0,1).
Keywords: Fisher’s equation; Local stabilization; Impulse output feedback controller

Ning Chen, Yanqing Wang, Dong-Hui Yang,
Time-varying bang–bang property of time optimal controls for heat equation and its application,
Systems & Control Letters,
Volume 112,
2018,
Pages 18-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.008.
(http://www.sciencedirect.com/science/article/pii/S016769111730227X)
Abstract: In this paper, the bang–bang property of time optimal controls for heat equation is established. Compared with the existing results on these problems, the bound of control variables is not a constant but a time-varying function. As an application of the bang–bang property, some kind of relation between the time optimal control problem and its corresponding target optimal control problem is considered.
Keywords: Heat equation; Bang–bang property; Time optimal control problem; Target optimal control problem

Tyler Homer, Prashant Mhaskar,
Constrained control Lyapunov function-based control of nonlinear systems,
Systems & Control Letters,
Volume 110,
2017,
Pages 55-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117301871)
Abstract: In this paper, we present an algorithm to address the problem of guaranteed stabilization of nonlinear systems from the largest set of initial conditions from where stabilization is possible, the so-called null controllable region (NCR), while also handling state constraints and partial unboundedness of the NCR. The controller uses the geometry of the NCR to inform a constrained control Lyapunov function which in turn provides feasibility and stability guarantees. The NCR is produced from a novel iterative growth algorithm that exploits a certain invariance property. The new controller implementation is illustrated using a chemical reactor system and compared to a conventional nonlinear model predictive control (MPC) implementation.
Keywords: Constrained control Lyapunov functions; Reachable sets; Nonlinear control; Constrained control; Null controllable region; Model predictive control

Mohamadreza Ahmadi, Hamed Mojallali, Rafael Wisniewski,
On robust stability of switched systems in the context of Filippov solutions,
Systems & Control Letters,
Volume 109,
2017,
Pages 17-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117301597)
Abstract: We consider the robust stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching. Instead of the Carathéodory solutions, we study the more general Filippov solutions. This encapsulates solutions with infinite switching in finite time and sliding modes in the neighborhood of the switching surfaces. In this regard, we formulate a Lyapunov-like stability theorem, based on the theory of differential inclusions. Additionally, we extend the results to switched systems with simplical uncertainty. We also demonstrate that, for the special case of polynomial switched systems defined on semi-algebraic sets, stability analysis can be checked based on sum of squares programming techniques.
Keywords: Switched systems; Sum of squares programming; Robust stability; Filippov solutions

Douglas A. Allan, Cuyler N. Bates, Michael J. Risbeck, James B. Rawlings,
On the inherent robustness of optimal and suboptimal nonlinear MPC,
Systems & Control Letters,
Volume 106,
2017,
Pages 68-78,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.005.
(http://www.sciencedirect.com/science/article/pii/S016769111730049X)
Abstract: Suboptimal model predictive control (MPC) is a control algorithm that uses suboptimal solutions to optimal control problems to provide control actions quickly. In MPC, terminal control laws and terminal region constraints are frequently used to ensure recursive feasibility and stability. Suboptimal MPC was proven to be inherently robust for systems with soft terminal region constraints in Pannocchia et al. (2011). We extend that work to systems with hard terminal region constraints. If these hard constraints are defined as sublevel sets of appropriate terminal cost functions, a well-chosen initial guess (warm start) for the optimization algorithm is robustly feasible. As a result, the system controlled by suboptimal MPC admits an ISS-Lyapunov function and is therefore inherently robust. The authors of Yu et al. (2014) noted that the result in Pannocchia et al. (2011) applied only to systems with continuous optimal cost functions. However, discontinuous optimal cost functions may be present in systems with hard terminal region constraints. We include a simple example of a continuous dynamical system with a provably discontinuous optimal value function that, as a consequence of the main result of this work, is inherently robust. This example is to our knowledge the first such system reported in the literature.
Keywords: Robust stability; Suboptimal model predictive control; Difference inclusions; Inherent robustness; Terminal constraints

Yu Huang, Xingfu Zhong,
Carathéodory–Pesin structures associated with control systems,
Systems & Control Letters,
Volume 112,
2018,
Pages 36-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117302281)
Abstract: We introduce five Carathéodory–Pesin (C–P) structures for control systems and show that the invariance entropy studied by Colonius and Kawan (2009) and the topological feedback entropy in Colonius et al., (2013) are just quantities generated by some special C–P structures that give the characteristics of dimension types for these classical control entropies. We explore some basic properties of these control entropies and investigate the relationships among these quantities. In addition, we also obtain a sufficient condition for the existence of a generator for the invariance entropy, which was posed by Kawan (2013, p. 87) as an open question.
Keywords: Dimension type; Invariance entropy; Topological feedback entropy

Lijuan Chen, Jitao Sun,
Distributed optimal control and L2 gain performance for the multi-agent system with impulsive effects,
Systems & Control Letters,
Volume 113,
2018,
Pages 65-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.007.
(http://www.sciencedirect.com/science/article/pii/S0167691118300082)
Abstract: In this paper, we investigate the distributed optimal control and L2 gain performance for the multi-agent system with impulsive effects. First, we obtain sufficient conditions to ensure that the distributed protocols can minimize the desired performance index with state-control cross weighting terms. Second, we propose and solve the bounded L2 gain synchronization problem for the impulsive system with hybrid disturbance inputs. Finally, an example is presented to illustrate the efficiency of the obtained results.
Keywords: Multi-agent system; Impulsive effect; Distributed optimal control; 
               L2 gain performance; Cross weighting term

H. Hammouri, F.S. Ahmed, S. Othman,
Observer design based on immersion technics and canonical form,
Systems & Control Letters,
Volume 114,
2018,
Pages 19-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691118300240)
Abstract: A crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system, and the analytical expression of the inverse of the immersion is unknown. In this paper, we have proposed a method for constructing observers for such autonomous nonlinear systems.
Keywords: Nonlinear system; Immersion; Observer

Li Sheng, Zidong Wang, Lei Zou,
Output-feedback H2∕H∞ consensus control for stochastic time-varying multi-agent systems with (x,u,v)-dependent noises,
Systems & Control Letters,
Volume 107,
2017,
Pages 58-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117301226)
Abstract: In this paper, the output feedback H2∕H∞ consensus control problem is investigated for discrete time-varying stochastic multi-agent systems with state, control and disturbance-dependent noises (also called (x,u,v)-dependent noises). Two new concepts for the H2 and H∞ consensus requirements are proposed to quantify the transient behavior of the consensus, over a finite horizon, for the addressed time-varying multi-agent systems. We aim to design an output feedback consensus controller such that the closed-loop multi-agent systems achieve the prescribed H2 and H∞ consensus performances over a finite horizon. By using the completing squares method and stochastic analysis techniques, sufficient conditions are derived for the existence of the desired output-feedback H2∕H∞ consensus controller in terms of the solution to two coupled backward recursive Riccati difference equations (RDEs). Moreover, an iterative algorithm is proposed for solving the RDEs by resorting to the Moore–Penrose pseudo inverse. A numerical example is utilized to illustrate the effectiveness of the proposed H2∕H∞ consensus control strategy.
Keywords: Multi-agent systems; Time-varying stochastic systems; 
               H2∕H∞ consensus control; Output feedback control; 
               (x,u,v)-dependent noises

Changliu Liu, Masayoshi Tomizuka,
Real time trajectory optimization for nonlinear robotic systems: Relaxation and convexification,
Systems & Control Letters,
Volume 108,
2017,
Pages 56-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117301469)
Abstract: Real time trajectory optimization is critical for robotic systems. Due to nonlinear system dynamics and obstacles in the environment, the trajectory optimization problems are highly nonlinear and non convex, hence hard to be computed online. Liu, Lin and Tomizuka proposed the convex feasible set algorithm (CFS) to handle the non convex optimization in real time by convexification. However, one limitation of CFS is that it will not converge to local optima when there are nonlinear equality constraints. In this paper, the slack convex feasible set algorithm (SCFS) is proposed to handle the nonlinear equality constraints, e.g. nonlinear system dynamics, by introducing slack variables to relax the constraints. The geometric interpretation of the method is discussed. The feasibility and convergence of the SCFS algorithm is proved. It is demonstrated that SCFS performs better than existing non convex optimization methods such as interior-point, active set and sequential quadratic programming, as it requires less computation time and converges faster.
Keywords: Optimal control; Nonlinear optimization; Non convex optimization; Motion planning

James Louisell,
Imaginary axis eigenvalues of matrix delay equations with a certain alternating coefficient structure,
Systems & Control Letters,
Volume 110,
2017,
Pages 49-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301901)
Abstract: In this paper we examine the imaginary axis eigenvalues of matrix delay differential equations with coefficients alternating between Hermitian and skew Hermitian, such as occurring in many mechanical systems. We show that given this special structure and a certain sign condition, the dimension of the eigenvalue problem is greatly reduced. We also give some theorems on eigenvalue crossing directions in this context, and show how reduction of dimension and crossing theorems work to provide insight on mechanical systems with time delay.
Keywords: Delay equation; Matrix polynomial; Stability switching

Huaibin Tang, Tao Li,
Convergence rates of discrete-time stochastic approximation consensus algorithms: Graph-related limit bounds,
Systems & Control Letters,
Volume 112,
2018,
Pages 9-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117302153)
Abstract: In this paper, we study the convergence rates of the discrete-time stochastic approximation consensus algorithms over sensor networks with communication noises under general digraphs. Basic results of stochastic analysis and algebraic graph theory are used to investigate the dynamics of the consensus error, and the mean square and sample path convergence rates of the consensus error are both given in terms of the graph and noise parameters. Especially, calculation methods to estimate the mean square limit bounds are presented under balanced digraphs, and sufficient conditions on the network topology and the step sizes are given to achieve the fast convergence rate. For the sample path limit bounds, estimation methods are also presented under undirected graphs.
Keywords: Consensus; Sensor network; Martingale difference sequence; Stochastic approximation; Convergence rate

E. Bakolas,
Constrained minimum variance control for discrete-time stochastic linear systems,
Systems & Control Letters,
Volume 113,
2018,
Pages 109-116,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691118300227)
Abstract: We propose a computational scheme for the solution of the so-called minimum variance control problem for discrete-time stochastic linear systems subject to an explicit constraint on the 2-norm of the input (random) sequence. In our approach, we utilize a state space framework in which the minimum variance control problem is interpreted as a finite-horizon stochastic optimal control problem with incomplete state information. We show that if the set of admissible control policies for the stochastic optimal control problem consists exclusively of sequences of causal (non-anticipative) control laws that can be expressed as linear combinations of all the past and present outputs of the system together with its past inputs, then the stochastic optimal control problem can be reduced to a deterministic, finite-dimensional optimization problem. Subsequently, we show that the latter optimization problem can be associated with an equivalent convex program and in particular, a quadratically constrained quadratic program (QCQP), by means of a bilinear transformation. Finally, we present numerical simulations that illustrate the key ideas of this work.
Keywords: Minimum-variance control; Stochastic optimal control; Discrete-time stochastic systems; Convex optimization

Nikita Barabanov, Romeo Ortega,
On global asymptotic stability of ẋ=−ϕ(t)ϕ⊤(t)x with ϕ not persistently exciting,
Systems & Control Letters,
Volume 109,
2017,
Pages 24-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.005.
(http://www.sciencedirect.com/science/article/pii/S016769111730169X)
Abstract: We study global convergence to zero of the solutions of the nth order differential equation ẋ=ϕ(t)ϕ⊤(t)x. We are interested in the case when the vector ϕ is not persistently exciting, which is a necessary and sufficient condition for global exponential stability. In particular, we establish new necessary conditions on ϕ(t) for global asymptotic stability of the zero equilibrium of the “unexcited” system. A new sufficient condition, that is strictly weaker than the ones reported in the literature, is also established. Unfortunately, it is also shown that this condition is not necessary.
Keywords: Linear time-varying systems; Stability theory; Persistency of excitation

Hugo Leiva,
Controllability of the impulsive functional BBM equation with nonlinear term involving spatial derivative,
Systems & Control Letters,
Volume 109,
2017,
Pages 12-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117301585)
Abstract: For a broad class of control systems modeling real-life problems, delays and impulses are natural properties that do not modify their behavior. So, we conjecture that under certain conditions delays and abrupt changes as perturbations of a system do not modify properties such as controllability. In this regard, we prove the approximate controllability of the impulsive functional Benjamin–Bona–Mahony (BBM) equation with nonlinear term involving spatial derivative, this can be achieved using the technique avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval.
Keywords: Interior approximate controllability; Benjamin–Bona–Mahony equation with impulses and delay; Strongly continuous semigroup

Lorenzo Ntogramatzidis, Fabrizio Padula,
A general approach to the eigenstructure assignment for reachability and stabilizability subspaces,
Systems & Control Letters,
Volume 106,
2017,
Pages 58-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117301068)
Abstract: This paper is concerned with the problem of determining basis matrices for the supremal output-nulling, reachability and stabilizability subspaces, and the simultaneous computation of the associated friends that place the assignable closed-loop eigenvalues at desired locations. Our aim is to show that the Moore–Laub algorithm in Moore and Laub (1978) for the computation of these subspaces was stated under unnecessary restrictive assumptions. We prove the same result under virtually no system-theoretic hypotheses. This provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust, and as general as the standard ones based on the computation of sequences of subspaces.
Keywords: LTI systems; Eigenstructure assignment

Justin Fong, Ying Tan, Vincent Crocher, Denny Oetomo, Iven Mareels,
Dual-loop iterative optimal control for the finite horizon LQR problem with unknown dynamics,
Systems & Control Letters,
Volume 111,
2018,
Pages 49-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.11.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117302037)
Abstract: Achieving optimal performance over a finite-time horizon has gained a lot of attention in many engineering applications. Among them, the Finite Horizon Linear Quadratic Regulator (FHLQR) formulation for continuous-time linear time-varying systems has been well studied, with an optimal solution characterised by the Differential Riccati Equation (DRE). The solution of the DRE requires that the exact system dynamics are known. However, this assumption may not always hold, as the plant model might not be completely known or may change over time due to wear and tear. This paper proposes a dual-loop iterative algorithm to find the optimal solutions of the FHLQR formulation for continuous-time LTV systems. The inner loop utilises input trajectories based on an estimate of the optimal control gain with the addition of some excitation noise, and produces measured state trajectories. The outer loop improves the estimate of the optimal control gain utilising these measured state trajectories. It is shown in this work that with appropriate selection of the discretisation parameter T and the set of excitation signals, the proposed dual-loop iterative algorithm can converge to an arbitrarily small neighbourhood of the optimal solution. A simulation example demonstrates the effectiveness of the proposed method.
Keywords: Finite Horizon linear quadratic regulator; Continuous-time; Dual-loop iterative algorithm

Shun Chen, Daniel W.C. Ho, Ming Liu,
Consensus protocol for multiple delta operator systems,
Systems & Control Letters,
Volume 107,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117301184)
Abstract: This paper considers the consensus problem for multiple delta operator systems. The delta operator system is used for describing continuous time processes at rapid rate sampling. Moreover, it has been known to have a better model description than that of shift-operator-based approach. In this work, the consensus problem is first solved for multiple delta operator systems by using a distributed protocol. To achieve consensus, several important sufficient conditions are proposed for the fast sampling systems based on the parameters of sampling period and consensus strength. In addition, two distributed consensus protocols are constructed for both leaderless multiple delta operator systems and leader–follower multiple delta operator systems. Finally, the effectiveness of the theoretical analysis is illustrated by applying distributed consensus protocol to multi-agent systems.
Keywords: Delta operator; Consensus; Distributed protocol

Masaki Ogura, Victor M. Preciado,
Second-order moment-closure for tighter epidemic thresholds,
Systems & Control Letters,
Volume 113,
2018,
Pages 59-64,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.006.
(http://www.sciencedirect.com/science/article/pii/S0167691118300070)
Abstract: In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible–infected–susceptible (SIS) stochastic spreading process. A precise quantification of this decay rate is crucial for designing efficient strategies to contain epidemic outbreaks. However, existing lower-bounds on the decay rate based on first-order mean-field approximations are often accompanied by a large error resulting in inefficient containment strategies. To overcome this deficiency, we derive a lower-bound based on a second-order moment-closure of the stochastic SIS processes. The proposed second-order bound is theoretically guaranteed to be tighter than existing first-order bounds. We also present various numerical simulations to illustrate how our lower-bound drastically improves the performance of existing first-order lower-bounds in practical scenarios, resulting in more efficient strategies for epidemic containment.
Keywords: Complex networks; Spreading processes; Stochastic processes; Stability

S. Feng, P. Tesi,
Networked control systems under Denial-of-Service: Co-located vs. remote architectures,
Systems & Control Letters,
Volume 108,
2017,
Pages 40-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.08.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117301457)
Abstract: In this paper, we consider networked systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. Previous studies have shown that co-located architectures (control unit co-located with the actuators and networked sensor channel) can ensure a high level of robustness against DoS. However, co-location requires a wired or dedicated actuator channel, which could not meet flexibility and cost requirements. To overcome these limitations, we consider control architectures that approximate co-location while enable remote implementation (networked sensor and actuator channels). We analyze closed-loop stability and quantify the robustness “gap” between this architecture and the co-located one. The analysis framework is flexible enough to account for the case where control and sensor channels are shared as well as for the case where the two channels are independent and can be jammed at different time instants.
Keywords: Cyber–physical systems; Denial-of-Service; Networked control systems; Sampled-data control

Xiao Liang, Juanjuan Xu, Huanshui Zhang,
Solution to stochastic LQ control problem for Itô systems with state delay or input delay,
Systems & Control Letters,
Volume 113,
2018,
Pages 86-92,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.012.
(http://www.sciencedirect.com/science/article/pii/S0167691118300197)
Abstract: This paper is concerned with the linear quadratic (LQ) control problem for Itô stochastic systems with state delay or input delay. The main contribution is to give the explicit optimal LQ controllers for Itô stochastic systems with input delay and with state delay respectively. For the case of state delay, the optimal LQ controller is a linear function of the state at the current time and the past time. For the case of input delay, the optimal LQ controller is a linear function of the state and the past inputs. The key technology is to define the value function and complete the square based on the coupled differential equations.
Keywords: LQ control; State delay; Input delay; Itô stochastic system; Value function


Editorial Board,
Systems & Control Letters,
Volume 108,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30172-X.
(http://www.sciencedirect.com/science/article/pii/S016769111730172X)

Ahmet Cetinkaya, Tomohisa Hayakawa, Mohd Amir Fikri bin Mohd Taib,
Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion,
Systems & Control Letters,
Volume 113,
2018,
Pages 71-77,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.010.
(http://www.sciencedirect.com/science/article/pii/S0167691118300112)
Abstract: A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromy matrix of the closed-loop system, we obtain conditions under which the closed-loop system’s state converges towards a periodic solution under our proposed control law. We discuss the application of our results in stabilization of unstable periodic orbits of nonlinear systems and present numerical examples to illustrate the efficacy of our approach.
Keywords: Stabilization of periodic orbits; Periodic systems; Time-varying systems; Delayed feedback stabilization

Fahad Albalawi, Helen Durand, Panagiotis D. Christofides,
Distributed economic model predictive control with Safeness-Index based constraints for nonlinear systems,
Systems & Control Letters,
Volume 110,
2017,
Pages 21-28,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117301858)
Abstract: In this work, sequential and iterative distributed economic model predictive control (DEMPC) architectures are developed with constraints based on a metric (termed the Safeness Index) that is indicative of the safeness of operating a process at a given state in state-space. The DEMPC’s may have lower computation times than a centralized economic model predictive control (EMPC) design with Safeness Index-based constraints, without significantly limiting closed-loop economic performance, which enhances their practicality and ability to improve process operational safety. Sufficient conditions are derived under which the implementation strategies for the DEMPC’s guarantee closed-loop stability.
Keywords: Economic model predictive control; Safety; Distributed control; Process control; Nonlinear systems

Xu Jin,
Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults,
Systems & Control Letters,
Volume 107,
2017,
Pages 100-109,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117301251)
Abstract: In this work, we present a novel control algorithm for a class of stochastic nonlinear systems with constraint requirement on the system output tracking error. The gain functions are not totally known, and the systems are subject to actuator faults. A novel structure of barrier Lyapunov function is proposed to deal with the constraint requirement in stochastic systems. We show that under the proposed control scheme, convergence of the system output tracking error into a small set around zero is guaranteed in the sense of mean quartic value. The constraint requirement on the system output tracking error will not be violated during operation in the sense of probability. The proposed scheme is also a unified approach, which can handle both deterministic and stochastic nonlinear systems of a particular structure, and can also handle nonlinear systems with or without system output constraint requirements. An illustrative example with both deterministic and stochastic nonlinear systems is presented to further demonstrate the effectiveness of the proposed control scheme.
Keywords: Stochastic nonlinear systems; Barrier Lyapunov function; Output constraint; Backstepping design; Actuator faults

Le Van Hien, Le Huy Vu, Hieu Trinh,
Stability of two-dimensional descriptor systems with generalized directional delays,
Systems & Control Letters,
Volume 112,
2018,
Pages 42-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.12.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117302220)
Abstract: This paper is concerned with the problem of stability analysis of two-dimensional (2-D) descriptor systems described by a Roesser-type model with generalized directional time-varying delays. By constructing an improved 2-D Lyapunov–Krasovskii functional candidate and utilizing zero-type free matrix equations, new delay-dependent conditions are derived in terms of linear matrix inequalities (LMIs) to ensure that the system under consideration is regular, causal and internally stable. The obtained results are shown to extend the existing literature by numerical examples.
Keywords: 2-D descriptor systems; Roesser model; Interval delays; 2-D summation inequality

Mahmoud El Chamie, Behçet Açıkmeşe,
Safe Metropolis–Hastings algorithm and its application to swarm control,
Systems & Control Letters,
Volume 111,
2018,
Pages 40-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117301895)
Abstract: This paper presents a new method to synthesize safe reversible Markov chains via extending the classical Metropolis–Hastings (M–H) algorithm. The classical M–H algorithm does not impose safety upper bound constraints on the probability vector, discrete probability density function, that evolves with the resulting Markov chain. This paper presents a new M–H algorithm for Markov chain synthesis that ensures such safety constraints together with reversibility and convergence to a desired stationary (steady-state) distribution. Specifically, we provide a convex synthesis method that incorporates the safety constraints via designing the proposal matrix for the M–H algorithm. It is shown that the M–H algorithm with this proposal matrix, safe M–H algorithm, ensures safety for a well-characterized convex set of stationary probability distributions, i.e., it is robustly safe with respect to this set of stationary distributions. The size of the safe set is then incorporated in the design problem to further enhance the robustness of the synthesized M–H proposal matrix. Numerical simulations are provided to demonstrate that multi-agent systems, swarms, can utilize the safe M–H algorithm to control the swarm density distribution. The controlled swarm density tracks time-varying desired distributions, while satisfying the safety constraints. Numerical simulations suggest that there is insignificant trade-off between the speed of convergence and the robustness.
Keywords: Markov chains; Metropolis–Hastings; Safety constraints; Convex optimization; Swarm control

Solmaz S. Kia,
Distributed optimal in-network resource allocation algorithm design via a control theoretic approach,
Systems & Control Letters,
Volume 107,
2017,
Pages 49-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.012.
(http://www.sciencedirect.com/science/article/pii/S0167691117301378)
Abstract: In this paper, we consider an in-network optimal resource allocation problem with multiple demand equations. We propose a novel distributed continuous-time algorithm that solves the problem over strongly connected and weight-balanced digraph network topologies when the local cost functions are strongly convex. We also discuss the extension of our convergence guarantees to dynamically changing topologies. Finally, we show that if the network is an undirected connected graph, we can guarantee stability and convergence of our algorithm for problems involving local convex functions. This convergence guarantee is to a point in the set of minimizers of our optimal resource allocation problem. The design and analysis of our algorithm are carried out using a control theoretic approach. We demonstrate our results through a numerical example.
Keywords: Cooperative control; Distributed convex optimization; Distributed optimal resource allocation; Strongly connected and weight-balanced digraphs

Tomás Caraballo, Mohamed Ali Hammami, Lassaad Mchiri,
Practical exponential stability of impulsive stochastic functional differential equations,
Systems & Control Letters,
Volume 109,
2017,
Pages 43-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.09.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117301809)
Abstract: This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional differential equations. The main tool used to prove the results is the Lyapunov–Razumikhin method which has proven very useful in dealing with stability problems for differential systems when the delays involved in the equations are not differentiable but only continuous. An illustrative example is also analyzed to show the applicability and interest of the main results.
Keywords: Impulsive stochastic functional differential equations; Almost sure practical exponential stability; Lyapunov–Razumikhin method

Christian Clason, Armin Rund, Karl Kunisch,
Nonconvex penalization of switching control of partial differential equations,
Systems & Control Letters,
Volume 106,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117301007)
Abstract: This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is penalization, in particular using L1-type norms. Applying this approach to the switching constraint leads to a nonsmooth and nonconvex infinite-dimensional minimization problem which is challenging both analytically and numerically. Adding H1 regularization or restricting to a finite-dimensional control space allows showing existence of optimal controls. First-order necessary optimality conditions are then derived using tools of nonsmooth analysis. Their solution can be computed using a combination of Moreau–Yosida regularization and a semismooth Newton method. Numerical examples illustrate the properties of this approach.
Keywords: Optimal control; Switching control; Partial differential equations; Nonsmooth optimization; Nonconvex analysis; Semi-smooth Newton method

Jianhui Huang, Haiyang Wang, Zhen Wu,
A sufficient stochastic maximum principle for a kind of recursive optimal control problem with obstacle constraint,
Systems & Control Letters,
Volume 114,
2018,
Pages 27-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691118300264)
Abstract: In this paper, we study a kind of recursive optimal control problem whose utility functional is described by the solution of a reflected backward stochastic differential equation (BSDE). We obtain a sufficient stochastic maximum principle of optimal controls. Moreover, a mixed optimal control problem is considered to illustrate the application of our theoretical result and the optimal control and stopping strategy are given.
Keywords: Maximum principle; Reflected backward stochastic differential equations; Recursive optimal control problems; Mixed control problems; Clarke’s generalized gradient

Shun-Pin Hsu,
Constructing a controllable graph under edge constraints,
Systems & Control Letters,
Volume 107,
2017,
Pages 110-116,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.015.
(http://www.sciencedirect.com/science/article/pii/S0167691117301408)
Abstract: This paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints. Specifically, suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given. We consider the problem of exploring a class of feasible graphs that satisfy the constraints. Using the hybrid of a path graph and an antiregular graph we propose a simple and systematic method to generate a class of controllable graphs whose diameters or degrees cover the full possible ranges. The method to select the control vector to ensure the controllability of the combined graph is also proposed. Numerical examples are provided to demonstrate our results.
Keywords: Controllability; Multi-agent systems; Threshold graph; Path graph

Jamila Kalantarova, Türker Özsarı,
Finite-parameter feedback control for stabilizing the complex Ginzburg–Landau equation,
Systems & Control Letters,
Volume 106,
2017,
Pages 40-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.004.
(http://www.sciencedirect.com/science/article/pii/S016769111730107X)
Abstract: In this paper, we prove the exponential stabilization of solutions for complex Ginzburg–Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg–Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.
Keywords: Ginzburg–Landau equations; Feedback stabilization; Finite volume elements; Finitely many Fourier modes; Nodal observables


Editorial Board,
Systems & Control Letters,
Volume 107,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30148-2.
(http://www.sciencedirect.com/science/article/pii/S0167691117301482)

Linlin Hou, Xudong Zhao, Haibin Sun, Guangdeng Zong,
l2−l∞ filtering of discrete-time switched systems via admissible edge-dependent switching signals,
Systems & Control Letters,
Volume 113,
2018,
Pages 17-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117301883)
Abstract: The problems of stability and l2−l∞ filtering are studied in this paper for a class of discrete-time switched systems. A novel admissible edge-dependent average dwell time switching is proposed on the basis of the directed graph. A condition ensuring the global uniform exponential stability of discrete-time switched systems is established. A new inequality that depicted the relation between Lyapunov-like function and disturbances is presented to guarantee the l2−l∞ performance. Combined with the multiple Lyapunov-like function technology, the filtering error system is proved to be globally uniformly exponentially stable with l2−l∞ performance, and the corresponding filter can also be obtained. Finally, three numerical examples are illustrated to show the effectiveness of the proposed results.
Keywords: Admissible edge-dependent average dwell time; Multiple Lyapunov-like functions; Discrete-time switched system; 
               l2−l∞ filter

Boris Houska, Matthias A. Müller,
Cost-to-travel functions: A new perspective on optimal and model predictive control,
Systems & Control Letters,
Volume 106,
2017,
Pages 79-86,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.06.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117301081)
Abstract: This paper concerns a class of functions, named cost-to-travel functions, which find applications in model-based control. For a given (potentially nonlinear) control system, the cost-to-travel function associates with any given start and end point in the state space and any given travel duration the minimum economic cost of the associated point-to-point motion. Cost-to-travel functions are a generalization of cost-to-go functions, which are often used in the context of dynamic programming as well as model predictive control. We discuss the properties of cost-to-travel functions, their relations to existing concepts in control such as dissipativity, but also a variety of control-theoretic applications of this function class. In particular, we discuss how cost-to-travel functions can be used to analyze the properties of economic model predictive control with return constraints.
Keywords: Optimal control; Model predictive control; Dissipativity


Editorial Board,
Systems & Control Letters,
Volume 110,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30205-0.
(http://www.sciencedirect.com/science/article/pii/S0167691117302050)

Francesca C. Chittaro, Jean-Paul Gauthier,
Asymptotic ensemble stabilizability of the Bloch equation,
Systems & Control Letters,
Volume 113,
2018,
Pages 36-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.01.008.
(http://www.sciencedirect.com/science/article/pii/S0167691118300094)
Abstract: In this paper we are concerned with the stabilizability at an equilibrium point of an ensemble of non interacting half-spins. We assume that the spins are immersed in a static magnetic field, with dispersion in the Larmor frequency, and are controlled by a time varying transverse field. Our goal is to steer the whole ensemble to the uniform “down” position. Two cases are addressed: for a finite ensemble of spins, we provide a control function (in feedback form) that asymptotically stabilizes the ensemble to the “down” position, generically with respect to the initial condition. For an ensemble containing a countable number of spins, we construct a sequence of control functions such that the sequence of the corresponding solutions pointwise converges, asymptotically in time, to the target state, generically with respect to the initial conditions. The control functions proposed are uniformly bounded and continuous.
Keywords: Ensemble controllability; Quantum control

Boris Andrievsky, Alexander L. Fradkov, Daniel Liberzon,
Robustness of Pecora–Carroll synchronization under communication constraints,
Systems & Control Letters,
Volume 111,
2018,
Pages 27-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117301998)
Abstract: We study synchronization of nonlinear systems with robustness to disturbances that arise when measurements sent from the master system to the slave system are affected by quantization and time sampling. Viewing the synchronization problem as an observer design problem, we invoke a recently developed theory of nonlinear observers robust to output measurement disturbances and formulate a sufficient condition for robust synchronization. The approach is illustrated by a detailed analysis of the Pecora–Carroll synchronization scheme for the Lorenz system, for which an explicit bound on the synchronization error depending on the quantizer range and sampling period is derived.

Guangming Zhuang, Qian Ma, Baoyong Zhang, Shengyuan Xu, Jianwei Xia,
Admissibility and stabilization of stochastic singular Markovian jump systems with time delays,
Systems & Control Letters,
Volume 114,
2018,
Pages 1-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2018.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691118300252)
Abstract: This paper deals with the admissibility analysis and stabilization of stochastic singular Markovian jump systems (SSMJSs) with time delays. More general conditions for the existence and uniqueness of the impulse-free solution to delayed SSMJSs are presented. Consequently, by constructing stochastic Lyapunov–Krasovskii functional and applying generalized Itô formula, new sufficient conditions for the stability of SSMJSs and delayed SSMJSs are obtained in terms of strict linear matrix inequalities. State feedback controller is designed to ensure stabilization of the delayed SSMJSs. Three illustrative examples, including an RLC circuit network and an oil catalytic cracking process, are employed to verify the effectiveness and usefulness of the obtained results.
Keywords: Stochastic singular systems; Markovian jump systems; Time-delay systems; Stochastic admissibility; State feedback control

Jinshan Zeng, Tao He, Mingwen Wang,
A fast proximal gradient algorithm for decentralized composite optimization over directed networks,
Systems & Control Letters,
Volume 107,
2017,
Pages 36-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.07.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117301238)
Abstract: This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form, and are possibly nonconvex. Examples of such problems include decentralized compressed sensing and constrained quadratic programming problems, as well as many decentralized regularization problems. We extend the existing algorithms PG-EXTRA and ExtraPush to a new algorithm PG-ExtraPush for composite consensus optimization over a directed network. This algorithm takes advantage of the proximity operator like in PG-EXTRA to deal with the nonsmooth term, and employs the push-sum protocol like in ExtraPush to tackle the bias introduced by the directed network. With a proper step size, we show that PG-ExtraPush converges to an optimal solution at a linear rate under some regular assumptions. We conduct a series of numerical experiments to show the effectiveness of the proposed algorithm. Specifically, with a proper step size, PG-ExtraPush performs linear rates in most of cases, even in some nonconvex cases, and is significantly faster than Subgradient-Push, even if the latter uses a hand-optimized step size. The established theoretical results are also verified by the numerical results.
Keywords: Decentralized optimization; Directed network; Composite objective; Nonconvex; Consensus

Said Aoues, Michael Di Loreto, Damien Eberard, Wilfrid Marquis-Favre,
Hamiltonian systems discrete-time approximation: Losslessness, passivity and composability,
Systems & Control Letters,
Volume 110,
2017,
Pages 9-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.003.
(http://www.sciencedirect.com/science/article/pii/S016769111730186X)
Abstract: In this paper a passive integrator dedicated to input/output Hamiltonian systems approximation is presented. In a first step, a discrete Hamiltonian framework endowed with a Lie derivative-like formula is introduced. It is shown that the discrete dynamics encodes energy conservation and passivity. Additionally, the characterization of the discrete dynamics in terms of Dirac structure is shown to be invariant by interconnection. The class is thus composable: networked systems belong to the class. In a second step, the discrete dynamics is considered as a one-step integration method. The method is shown to be convergent and provides a discrete-time approximation of an input/output Hamiltonian system. Accordingly, the discrete dynamics inherits intrinsic energetic characteristics (storage function and dissipation rate) from the original system. The method is thus tagged as passive integrator. As an illustration, the closed-loop behavior of interconnected subsystems and the stabilization of a rigid body spinning around its center of mass are presented.
Keywords: Hamiltonian difference scheme; Energetic integrator; Passive integrator; Dirac structure; Composability

Huabin Chen, Peng Shi, Cheng-Chew Lim,
Stability analysis for neutral stochastic delay systems with Markovian switching,
Systems & Control Letters,
Volume 110,
2017,
Pages 38-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301913)
Abstract: This paper considers the exponential stability in pth(p≥1) moment and the almost sure exponential stability for neutral stochastic delay systems with Markovian switching. By using the generalized integral inequality and the nonnegative local martingale convergence theorem, the Lyapunov stability results on the exponential stability in pth(p≥1) moment and the almost sure exponential stability for such systems are given when the time-varying delay is a bounded measurable function and the coefficients in the monotonicity condition are time varying. The derived results are illustrated by two examples.
Keywords: Neutral stochastic delay systems; Time-varying delay; Exponential stability; Almost sure exponential stability; Markovian switching

Christian Commault, Jacob van der Woude, Taha Boukhobza,
On the fixed controllable subspace in linear structured systems,
Systems & Control Letters,
Volume 102,
2017,
Pages 42-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117300063)
Abstract: In this paper we consider interconnected networks that are described by means of structured linear systems with state and control variables. We represent these systems, whose matrices contain fixed zeros and free parameters, by means of directed graphs and study questions concerning controllability and the controllable subspace. We show in this paper that the controllable subspace can have a part that will be present for almost all values of the free parameters. It actually is a subspace of the controllable subspace and will be referred to as the fixed controllable subspace. The subspace can then be seen as a kind of robustly controllable part of the system. Indeed, it is a subspace in the state space with the generic property that states in it can be steered in an arbitrary way. We derive a characterization of the fixed controllable subspace using the graph representation. The obtained characterization makes use of well-known algorithms from optimization and networks theory. To get some more insight in the components in the fixed part, we also give a representation of the structured linear systems by means of bipartite graphs. Using the Dulmage–Mendelsohn decomposition, we are able to decompose our structured systems in such a way that in some special cases, the fixed controllable subspace can be obtained directly from the decomposition.
Keywords: Controllability; Structured system theory; Graph theory

Siyun Wang, Jodie M. Simkoff, Michael Baldea, Leo H. Chiang, Ivan Castillo, Rahul Bindlish, David B. Stanley,
Autocovariance-based plant-model mismatch estimation for linear model predictive control,
Systems & Control Letters,
Volume 104,
2017,
Pages 5-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117300464)
Abstract: In this paper, we present autocovariance-based estimation as a novel methodology for determining plant-model mismatch for multiple-input, multiple-output systems operating under model predictive control. Considering discrete-time, linear time invariant systems under reasonable assumptions, we derive explicit expressions of the autocovariances of the system inputs and outputs as functions of the plant-model mismatch. We then formulate the mismatch estimation problem as a global optimization aimed at minimizing the discrepancy between the theoretical autocovariance estimates and the corresponding values computed from historical closed-loop operating data. Practical considerations related to implementing these ideas are discussed, and the results are illustrated with a chemical process case study.
Keywords: Model predictive control; Plant-model mismatch; Autocovariance

Fengwei Chen, Marion Gilson, Hugues Garnier, Tao Liu,
Robust time-domain output error method for identifying continuous-time systems with time delay,
Systems & Control Letters,
Volume 102,
2017,
Pages 81-92,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117300221)
Abstract: In this paper, an output error method is proposed for the identification of continuous-time systems with time delay from sampled data. The challenge of time delay system identification lies in the presence of nonlinear time delays in models, then starting value-based optimization methods may be trapped easily by local minima. In order to improve the convergence performance to the choice of initial parameters, several approaches to smooth the loss function are presented. It is shown that the loss function may possess many local minima when data are regularly sampled with the inter-sample behavior of zero-order hold. Interestingly, irregular sampling can be an efficient approach to overcome these local minima. To achieve superior convergence performance, an over-parametrization approach incorporating a low-pass filtering technique is proposed to enlarge the convergence region. Theoretical and simulated results are presented to demonstrate the effectiveness of the proposed method.
Keywords: Continuous-time system; Identification; Time delay; Output error method; Irregular sampling

Christopher Beattie, Serkan Gugercin, Volker Mehrmann,
Model reduction for systems with inhomogeneous initial conditions,
Systems & Control Letters,
Volume 99,
2017,
Pages 99-106,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116301864)
Abstract: We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a superposition of the response map for an unforced system having nontrivial initial conditions and the response map for a forced system having null initial conditions, we develop a new approach that involves reducing these component responses independently and then combining the reduced responses into an aggregate reduced system response. This approach allows greater flexibility and offers better approximation properties than other comparable methods.
Keywords: Model reduction; Inhomogeneous initial condition; Balanced truncation; Transfer map splitting; Approximation error balancing; Iterative rational Krylov algorithm

R. Altmann, P. Schulze,
A port-Hamiltonian formulation of the Navier–Stokes equations for reactive flows,
Systems & Control Letters,
Volume 100,
2017,
Pages 51-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301980)
Abstract: We consider the problem of finding an energy-based formulation of the Navier–Stokes equations for reactive flows. These equations occur in various applications, e. g., in combustion engines or chemical reactors. After modeling, discretization, and model reduction, important system properties as the energy conservation are usually lost which may lead to unphysical simulation results. In this paper, we introduce a port-Hamiltonian formulation of the one-dimensional Navier–Stokes equations for reactive flows. The port-Hamiltonian structure is directly associated with an energy balance, which ensures that a temporal change of the total energy is only due to energy flows through the boundary. Furthermore, the boundary ports may be used for control purposes.
Keywords: Reactive flow; Port-Hamiltonian formulation; Navier–Stokes equations; Hamiltonian formulation; Energy-Based modeling

Parijat Bhowmick, Sourav Patra,
On LTI output strictly negative-imaginary systems,
Systems & Control Letters,
Volume 100,
2017,
Pages 32-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301979)
Abstract: This paper deals with the notion of output strictly negative-imaginary systems. A definition is given for the class of output strictly negative-imaginary systems and a lemma is proposed to test the necessary and sufficient conditions required to satisfy output strictly negative-imaginary system properties. A set theoretic relationship is established between the existing class of strictly negative-imaginary systems and the newly defined output strictly negative-imaginary systems class. A stability analysis result for interconnected systems with positive feedback is presented while one of the systems is negative-imaginary and the other one is output strictly negative-imaginary, contrary to the existing results where at least one of the systems in the interconnection belongs to the strictly negative-imaginary class. Several numerical examples have been studied to demonstrate the proposed results.
Keywords: Output strictly negative-imaginary systems; Output strict passivity; 
               (Q,S,R)-dissipativity; Positive feedback; Interconnected system; Robust stability

Noorma Yulia Megawati, Arjan van der Schaft,
Abstraction and control by interconnection of linear systems: A geometric approach,
Systems & Control Letters,
Volume 105,
2017,
Pages 27-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117300853)
Abstract: We consider the problem of constructing a controller achieving a desired linear specification, based on a linear abstraction system of the plant system. First, we extend the necessary and sufficient conditions for control by interconnection by bisimulation equivalence to the case of non-deterministic linear systems. Then we apply the controller constructed on the basis of the lower-dimensional abstraction system to the original plant system and show that the closed-loop system is simulated by the given specification system. We distinguish between two forms of abstraction of the plant system. In the first one, the set of variables available for controller interconnection remains the same. In the second, more general form, this is not anymore the case, and we show how an adapted form of interconnection of the controller system to the plant system yields the same result.
Keywords: Abstraction; Simulation relation; Control by interconnection; Canonical controller; Bisimilar


Editorial Board,
Systems & Control Letters,
Volume 101,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30033-6.
(http://www.sciencedirect.com/science/article/pii/S0167691117300336)

Henrik Anfinsen, Ole Morten Aamo,
Adaptive output-feedback stabilization of linear 2×2 hyperbolic systems using anti-collocated sensing and control,
Systems & Control Letters,
Volume 104,
2017,
Pages 86-94,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117300610)
Abstract: We construct a control law that manages to adaptively stabilize a class of linear 2×2 hyperbolic systems of partial differential equations (PDEs) from a single boundary sensing anti-collocated with the boundary where actuation takes place. We do this by introducing a series of invertible transformations that bring the system into an observer canonical form, for which adaptive control design becomes feasible. We establish pointwise boundedness of all signals in the closed loop system, and pointwise convergence of the system states to zero. The theory is demonstrated in a simulation.
Keywords: Distributed systems; Adaptive control; Backstepping

P. Laakkonen, A. Quadrat,
A fractional representation approach to the robust regulation problem for SISO systems,
Systems & Control Letters,
Volume 103,
2017,
Pages 32-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117300294)
Abstract: The purpose of this article is to develop a new approach to the robust regulation problem for plants which do not necessarily admit coprime factorizations. The approach is purely algebraic and allows us dealing with a very general class of systems in a unique simple framework. We formulate the famous internal model principle in a form suitable for plants defined by fractional representations which are not necessarily coprime factorizations. By using the internal model principle, we are able to give necessary and sufficient solvability conditions for the robust regulation problem and to parameterize all robustly regulating controllers.
Keywords: Robust regulation; Fractional representation approach; Linear systems

Cong Wu, Xinzhi Liu,
External stability of switching control systems,
Systems & Control Letters,
Volume 106,
2017,
Pages 24-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117301020)
Abstract: This paper investigates external stability (defined by the normal L2 norm) of switching control systems. It proposes definitions of the maximum, minimum dwell time for switching systems and then derives an important relation between the number of switchings and the maximum, minimum dwell time. Applying this relation, it establishes criteria on external stability of switching control systems consisting of Hurwitz stable subsystems. Furthermore, a switching law is proposed, and is proven to be realizable. Given this proposed switching law and applying the previous derived relation, the switching control systems comprised of both Hurwitz stable and Hurwitz unstable subsystems are proved to be externally stable.
Keywords: External stability; Normal L2 norm; Switching system; Maximum dwell time; Minimum dwell time


Editorial Board,
Systems & Control Letters,
Volume 103,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30069-5.
(http://www.sciencedirect.com/science/article/pii/S0167691117300695)

Yong He,
Partial exact controllability for wave equations,
Systems & Control Letters,
Volume 103,
2017,
Pages 45-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117300452)
Abstract: We analyze the partial exact controllability problem for wave equations. The goal is to drive part of the solution to a destination at a given time. The main results are proved by employing the classical theory of propagation of singularities of wave equations and the compact uniqueness argument.
Keywords: Partial exact controllability; Wave equation

Khaled Bahlali, Meriem Mezerdi, Brahim Mezerdi,
Existence and optimality conditions for relaxed mean-field stochastic control problems,
Systems & Control Letters,
Volume 102,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.009.
(http://www.sciencedirect.com/science/article/pii/S016769111730004X)
Abstract: We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjoint processes extending the known results to the case of relaxed controls.
Keywords: Mean-field stochastic differential equation; Relaxed control; Martingale measure; Adjoint process; Stochastic maximum principle; Variational principle

Keith Glover, Andrew Packard,
Some numerical considerations in H∞ control,
Systems & Control Letters,
Volume 101,
2017,
Pages 15-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116300020)
Abstract: Certain H∞-control problems are considered and potential numerical difficulties are discussed. An alternative test for checking that the solution to an algebraic Riccati equation is positive semi-definite which is robust to rounding error even when the matrix is singular is presented. Finally the H∞ loop-shaping method is summarised and its numerical properties are shown to be satisfactory.
Keywords: H-infinity control; Numerical methods; Loop-shaping control

Delsin Menolascino, ShiNung Ching,
Bispectral analysis for measuring energy-orientation tradeoffs in the control of linear systems,
Systems & Control Letters,
Volume 102,
2017,
Pages 68-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117300051)
Abstract: Many characterizations of linear system controllability revolve around the eigenvalue spectrum of the controllability gramian, which is a function of the network dynamics. The gramian spectrum describes the minimum energies associated with inducing movement along orthogonal directions in Rn. Here, we derive an enhanced interpretation of the spectral properties of the gramian in non-minimum energy regimes. Indeed, in a non-minimum energetic regime, an ‘excess’ of energy is available to the system for at least (n−1) orthogonal state transfers. We show that the utility of this excess energy can be quantified in terms of input orientation, or, simply, the angle between two competing inputs. Based on this notion, we derive the gramian bispectrum, which describes the relationship between energy and orientation among pairs of orthogonal state transfers. The bispectrum reflects a fundamental tradeoff between the energetic and orientation costs in the control of a linear system. We show how this bispectral analysis can provide control characterizations that are not apparent from inspection of the gramian spectrum alone.
Keywords: Network analysis; Network control; Linear systems; Bispectrum

Shen Zeng, Frank Allgöwer,
A moment-based approach to ensemble controllability of linear systems,
Systems & Control Letters,
Volume 98,
2016,
Pages 49-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.020.
(http://www.sciencedirect.com/science/article/pii/S0167691116301475)
Abstract: In this paper we introduce a new perspective on the L2-ensemble controllability problem of linear time-invariant systems using an ℓ2-framework. The reformulation results from focussing on the controllability of the ensemble’s moments, which evolve under a linear system defined on the space of square-summable sequences. For a specific class of ensembles, a necessary and sufficient condition can be stated in terms of truncations of infinite Kalman matrices. We illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble’s moments, as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature.
Keywords: Linear systems; Ensemble controllability; Approximate controllability

Jan Maximilian Montenbruck, Shen Zeng,
Collinear dynamical systems,
Systems & Control Letters,
Volume 105,
2017,
Pages 34-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.008.
(http://www.sciencedirect.com/science/article/pii/S016769111730083X)
Abstract: We introduce and study collinearity as a systems theoretic property, asking whether coupled dynamical systems with collinear initial conditions maintain collinear solutions for all times. Completely characterizing such collinear dynamical systems, we find that they define a Lie algebra whose Lie group are the invertible collinearity-preserving maps. Our characterization of collinear systems then allows us to determine state feedbacks which enforce collinear solutions in coupled control systems. Further, we characterize coupled linear differential equations whose solutions will asymptotically become collinear. Last, we characterize collinearity of multiple dynamical systems and their ability to produce coplanar solutions. Our findings relate to flows on the real projective spaces and Grassmannians.
Keywords: Linear systems theory; Geometric approaches; Multi-agent systems

Francisco Javier Muros, Encarnación Algaba, José María Maestre, Eduardo F. Camacho,
The Banzhaf value as a design tool in coalitional control,
Systems & Control Letters,
Volume 104,
2017,
Pages 21-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117300609)
Abstract: In this paper, the game theory solution concept known as Banzhaf value is applied to games in coalitional control schemes. In these schemes, the network topology is modified to achieve a trade-off between performance and communication burden. In particular, we show how to design a coalitional scheme with constraints regarding the Banzhaf value. Several similarities and differences of this value with respect to the Shapley value are stated, and the concept of amalgamated game is introduced in coalitional control as a means to relieve the computational burden. Finally, an academic simulation example illustrates the results obtained in this work.
Keywords: Banzhaf value; Coalitional control; Distributed control; Cooperative game theory; Amalgamated games

Jochen Trumpf, Harry L. Trentelman,
A converse to the deterministic separation principle,
Systems & Control Letters,
Volume 101,
2017,
Pages 2-9,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.021.
(http://www.sciencedirect.com/science/article/pii/S0167691116000578)
Abstract: In the classical theory of finite-dimensional linear time-invariant systems in state space form the term deterministic separation principle refers to the observation that a stabilizing output feedback controller can be constructed by first constructing an asymptotic state observer that is then coupled to a stabilizing state feedback controller. In this paper we discuss the following converse problem: Can every stabilizing output feedback controller be realized as interconnection of an asymptotic state observer and a stabilizing state feedback controller? We will provide an affirmative answer to this question (modulo a number of technicalities) in a behavioral setting and with the help of rational representations.
Keywords: Separation principle; Output feedback; Linear systems; Behavioral approach

Fuchun Liu, Rixiang Mo,
Correctability of fault-tolerant stochastic discrete-event systems,
Systems & Control Letters,
Volume 105,
2017,
Pages 48-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117300841)
Abstract: Failure diagnosis and correction of discrete-event systems (DESs) have received considerable attention in recent years due to the practical and theoretical importance. As a continuation of our prior work on diagnosability of stochastic DESs (i.e., Liu et al., 2008; Liu and Qiu, 2008), this paper aims to investigate the correctability issue, where the considered system is equipped with a probabilistic structure to estimate the likelihood of events occurring. More specifically: (1) We formalize the notion of k-step corrective probability to calculate the correctability of stochastic systems. Roughly speaking, the k-step corrective probability represents the probability that the stochastic system may recover to accepted states from the current state within k steps. (2) By introducing the strategy of adjusting the transition probability of the current state of system, an optimal correction mechanism is presented to achieve the maximal k-step corrective probability. (3) In addition, a novel approach of the computation of supremal corrective probability is developed by constructing the decision tree after introducing the infinitely expandable states. Finally, an example for the evolution process of the voltage in a circuit system modeled by a stochastic automaton is provided to illustrate the proposed results.
Keywords: Failure diagnosis; Discrete-event systems; Stochastic system; Fault-tolerant system; Correctability

Michael Heinrich Baumann, Lars Grüne,
Simultaneously long short trading in discrete and continuous time,
Systems & Control Letters,
Volume 99,
2017,
Pages 85-89,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116301906)
Abstract: Simultaneously long short (SLS) feedback trading strategies are known to yield positive expected gain by zero initial investment for price processes governed by, e.g., geometric Brownian motion or Merton’s jump diffusion model. In this paper, we generalize these results to positive prices with stochastically independent multiplicative growth and constant trend in discrete and continuous time as well as for sampled-data systems and show that in all cases the SLS strategies’ expected gain does not depend on the price model but only on the trend.
Keywords: Feedback-based stock trading; Technical trading rules; Simultaneously long short strategy; Sampled-data systems; Lévy processes

Lin Zhao, Yingmin Jia, Jinpeng Yu,
Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions,
Systems & Control Letters,
Volume 102,
2017,
Pages 22-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117300087)
Abstract: This paper is concerned with the adaptive finite-time bipartite consensus problems for networked second-order multi-agent systems with antagonistic interactions and unknown external disturbances. A signed undirected graph is used to describe the interactions among agents. For the leaderless case, continuous nonlinear distributed protocols with adaptive update laws are given, which can not only guarantee the bipartite steady-state errors of any two agents converge to a small region in finite time, but also eliminate the chattering problem. Then, the proposed algorithm is extended to solve the adaptive finite-time bipartite consensus tracking problem for leader–follower case by designing distributed finite-time estimator. Simulation example is included to show the effectiveness of the presented methods.
Keywords: Cooperative and antagonistic interactions; Signed graphs; Bipartite consensus; Finite-time control; Adaptive control

Zhiqiang Miao, Yaonan Wang, Rafael Fierro,
Cooperative circumnavigation of a moving target with multiple nonholonomic robots using backstepping design,
Systems & Control Letters,
Volume 103,
2017,
Pages 58-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117300488)
Abstract: The problem of cooperative circumnavigation of a moving target with multiple nonholonomic robots is addressed in this paper. The goal for the multi-robot system is to circumnavigate the moving target with prescribed radius, circular velocity, and inter-robot angular spacing. Two distributed control strategies respectively in Cartesian coordinates and polar coordinates are proposed using backstepping techniques, in which some virtual signals are introduced to facilitate the control design. Under some mild assumptions on the velocity of the target, the proposed controllers ensure asymptotic convergence of the robot team to the desired motion. Explicit stability and convergence analyses are presented using Lyapunov tools. The effectiveness of the proposed control strategies is demonstrated through numerical simulations.
Keywords: Circumnavigation; Cooperative control; Nonholonomic robots; Multi-robot systems; Backstepping

Luca Consolini, Marco Locatelli, Andrea Minari, Aurelio Piazzi,
An optimal complexity algorithm for minimum-time velocity planning,
Systems & Control Letters,
Volume 103,
2017,
Pages 50-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117300245)
Abstract: Velocity planning on a path to be followed by a wheeled autonomous vehicle may be difficult when high curvatures and velocities are allowed. A fast, straightforward algorithm to address this problem is presented. It has linear-time computational complexity and provides an optimal minimum-time velocity profile. The algorithm is based on a curvilinear discretization that makes easy to take into account the constraint on the vehicle’s maximal normal acceleration. A generalized problem is also addressed with formal results on feasibility, complexity, and solution characterization. Three examples illustrate the proposed approach.
Keywords: Optimization; Motion planning; Minimum-time problems; Hidden convexity

Huiping Li, Weisheng Yan, Yang Shi,
A receding horizon stabilization approach to constrained nonholonomic systems in power form,
Systems & Control Letters,
Volume 99,
2017,
Pages 47-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301840)
Abstract: The control of nonholonomic systems with practical requirements is still a challenging problem but finds many industrial applications. This paper studies the receding horizon control (RHC)-based stabilization problem of a class of constrained nonholonomic systems in power form. A non-quadratic cost function is constructed by using the homogeneous norm of the nonholonomic system in power form. With this novel cost function, two kinds of RHC algorithms are designed, of which one ensures the convergence of the closed-loop system states, and the other ensures the ρ-exponential stability. The feasibility of the designed algorithms and the closed-loop convergence are analyzed and ensured theoretically under mild conditions. The comparison and application results are provided, showing that (1) the proposed RHC algorithms are effective and the theoretical results are valid, and (2) the proposed algorithms can stabilize the nonholonomic systems with a much faster convergence rate than the conventional time-varying stabilizable controllers.
Keywords: Receding horizon control (RHC); Nonholonomic systems; Input constraints; Stabilization; Nonlinear systems; 
               ρ-exponential stability

Jonathan Laporte, Antoine Chaillet, Yacine Chitour,
Global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives,
Systems & Control Letters,
Volume 99,
2017,
Pages 17-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116301682)
Abstract: In this paper, we address the problem of globally stabilizing a linear time-invariant (LTI) system by means of a static feedback law whose amplitude and successive time derivatives, up to a prescribed order p, are bounded by arbitrary prescribed values. We solve this problem for two classes of LTI systems, namely integrator chains and controllable skew-symmetric systems with single input. For the integrator chains, the solution we propose is based on the nested saturations introduced by A.R. Teel. We show that this construction fails for skew-symmetric systems and propose an alternative feedback law. We illustrate these findings by the stabilization of the third order integrator and the harmonic oscillator with prescribed bounds on the feedback and its first two derivatives.
Keywords: Global stabilization; Bounded controls; Rate saturation; Multiple integrators; Oscillators

Olumuyiwa I. Olanrewaju, Jan M. Maciejowski,
Implications of dissipativity on stability of economic model predictive control—The indefinite linear quadratic case,
Systems & Control Letters,
Volume 100,
2017,
Pages 43-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301839)
Abstract: In contrast to the conventional model predictive control (MPC) approach to control of a given system where a positive–definite objective function is employed, economic MPC employs a generic cost which is related to the ‘economics’ of the process as the objective function in the regulation layer. Often, stability proofs of the closed-loop system are based on strict-dissipativity of the system with respect to this objective function. In this paper, we focus on linear systems with indefinite quadratic costs. We show that while strict–dissipativity guarantees stability of the closed–loop system, it is not required. Hence we formulate a necessary and sufficient condition that guarantees asymptotic stability of the closed loop system. This condition comes down to the existence of two distinct storage functions for which the system is dissipative.
Keywords: Economic model predictive control; Dissipativity; Strict–dissipativity; Stability

Sorin Micu, Ademir F. Pazoto,
Stabilization of a Boussinesq system with generalized damping,
Systems & Control Letters,
Volume 105,
2017,
Pages 62-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.012.
(http://www.sciencedirect.com/science/article/pii/S0167691117300919)
Abstract: A family of Boussinesq systems was proposed by J. L. Bona, M. Chen and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. Our work considers a class of these Boussinesq systems which couples two Benjamin–Bona–Mahony with periodic boundary conditions. We study the stability properties of the resulting system when generalized damping operators are introduced in each equation. By means of spectral analysis and Fourier expansion, we prove that the solutions of the linearized system decay uniformly or not to zero, depending on the parameters of the damping operators. In the uniform decay case, we show that the same property holds for the nonlinear system.
Keywords: Boussinesq system; Benjamin–Bona–Mahony equation; Generalized damping; Stabilizability; Fourier expansion

Bao-Zhu Guo, Ze-Hao Wu,
Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control,
Systems & Control Letters,
Volume 100,
2017,
Pages 21-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116301955)
Abstract: In this paper, we apply active disturbance rejection control, an emerging control technology, to achieve practical output tracking for a class of nonlinear systems in the presence of vast matched and mismatched uncertainties including unknown internal system dynamic uncertainty, external disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The total disturbance influencing the performance of controlled output is refined first and then estimated by an extended state observer (ESO). Under the assumption that the inverse dynamics of the uncertain systems are bounded-input-bounded-state stable, a constant high gain ESO based output feedback is constructed to guarantee that the state is bounded and the output tracks practically a given reference signal. A time-varying gain ESO is also discussed to reduce the peaking value near the initial stages of ESO caused by constant high gain. Numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.
Keywords: Active disturbance rejection control; Output tracking; Extended state observer; Mismatched uncertainty

P.-Y. Chevalier, J.M. Hendrickx, R.M. Jungers,
Tight bound for deciding convergence of consensus systems,
Systems & Control Letters,
Volume 105,
2017,
Pages 78-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117300877)
Abstract: We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with period smaller than a certain value converge to zero. Moreover, bounds on that value are available (Lagarias and Wang, 1995). We provide a stronger bound that holds for both polyhedral norms and polyhedral seminorms. In the latter case, the matrix products do not necessarily converge to zero, but all trajectories of the associated system converge to a common invariant subspace. We prove that our bound is tight for all seminorms. Our work is motivated by problems in consensus systems, where the matrices are stochastic (nonnegative with rows summing to one), and hence always share a same common nonincreasing polyhedral seminorm. In that case, we also improve existing results.
Keywords: Stability of matrix sets; Stochastic matrices; Consensus

José L. Mancilla-Aguilar, Hernan Haimovich,
On zero-input stability inheritance for time-varying systems with decaying-to-zero input power,
Systems & Control Letters,
Volume 104,
2017,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117300634)
Abstract: Stability results for time-varying systems with inputs are relatively scarce, as opposed to the abundant literature available for time-invariant systems. This paper extends to time-varying systems existing results that ensure that if the input converges to zero in some specific sense, then the state trajectory will inherit stability properties from the corresponding zero-input system. This extension is non-trivial, in the sense that the proof technique is completely novel, and allows to recover the existing results under weaker assumptions in a unifying way.
Keywords: Nonlinear systems; Time-varying systems; Stability; Convergence; Omega-limit sets

Walid Djema, Frédéric Mazenc, Catherine Bonnet,
Stability analysis and robustness results for a nonlinear system with distributed delays describing hematopoiesis,
Systems & Control Letters,
Volume 102,
2017,
Pages 93-101,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117300117)
Abstract: A nonlinear system with distributed delays describing cell dynamics in hematopoiesis is analyzed–in the time-domain–via a construction of suitable Lyapunov–Krasovskii functionals (LKFs). Two interesting biological situations lead us to re-investigate the stability properties of two meaningful steady states: the 0-equilibrium for unhealthy hematopoiesis and the positive equilibrium for the healthy case. Biologically, convergence to the 0-equilibrium means the extinction of all the generations of blood cells while the positive equilibrium reflects the normal process where blood cells survive. Their analyses are slightly different in the sense that we take advantage of positivity of the system to construct linear functionals to analyze the 0-equilibrium, while we use some quadratic functionals to investigate the stability properties of the positive equilibrium. For both equilibria, we establish the exponential stability of solutions and we provide an estimate of their rates of convergence. Moreover, a robustness analysis is performed when the model is subject to some nonvanishing perturbations. Numerical examples are provided.
Keywords: Delay; Positive system; Lyapunov; Stability; Biological model


Editorial Board,
Systems & Control Letters,
Volume 102,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30051-8.
(http://www.sciencedirect.com/science/article/pii/S0167691117300518)

Shaolin Ji, Xiaomin Shi,
Explicit solutions for continuous time mean–variance portfolio selection with nonlinear wealth equations,
Systems & Control Letters,
Volume 104,
2017,
Pages 1-4,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117300592)
Abstract: This paper concerns the continuous time mean–variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in Ji (2010) does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of the HJB equation. Furthermore, via this explicit viscosity solution, we obtain explicitly the efficient portfolio strategy and efficient frontier for this problem. Finally, we show that our nonlinear wealth equation can cover three important cases.
Keywords: Mean–variance portfolio selection; Nonlinear wealth equation; HJB equation; Viscosity solution

Matthew C. Turner,
Positive μ modification as an anti-windup mechanism,
Systems & Control Letters,
Volume 102,
2017,
Pages 15-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117300075)
Abstract: This paper proposes a simple anti-windup mechanism for a model reference adaptive control scheme subject to saturation constraints. The anti-windup compensator has, in essence, the same structure as positive μ modification for the same class of systems. It is shown how this structure can, under certain circumstances, display characteristics similar to anti-windup schemes proposed for linear control systems. In particular, it is shown that if the (unknown) ideal control signal eventually lies within the control constraints, then the response of the adaptive control system will converge to that of the reference system—provided certain conditions are satisfied. The paper illustrates the challenge of designing anti-windup compensators for model-reference adaptive control systems.
Keywords: Adaptive control; Anti-windup; Saturation

Kaihong Yang, Haibo Ji,
Hierarchical analysis of large-scale control systems via vector simulation function,
Systems & Control Letters,
Volume 102,
2017,
Pages 74-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117300233)
Abstract: In this paper, we study the hierarchical problem of large-scale control systems. As a natural extension of traditional simulation function, the new notion of vector simulation function is introduced for investigating the hierarchies between abstract systems and concrete systems. By constructing a comparison system, we present a generalized result on this problem which, in the case of a scalar simulation function, specializes to the classical result. When interconnected nonlinear systems are considered, an easily checkable sufficient condition is obtained to facilitate the compositional construction of abstractions. Based on the condition, we propose a particular construction of abstractions for interconnected linear systems. Finally, two examples are included.
Keywords: Large-scale control system; Vector simulation function; Hierarchical analysis; Abstraction

Andrii Mironchenko,
Uniform weak attractivity and criteria for practical global asymptotic stability,
Systems & Control Letters,
Volume 105,
2017,
Pages 92-99,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117300993)
Abstract: A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ. We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attractive set. This result is valid for a wide class of distributed parameter systems, including time-delay systems, switched systems, many classes of PDEs and evolution differential equations in Banach spaces. We apply our results to show that existence of a non-coercive Lyapunov function ensures pUGAS for this class of systems. For ordinary differential equations with uniformly bounded disturbances, the concept of uniform weak attractivity is equivalent to the well-known notion of weak attractivity. It is however essentially stronger than weak attractivity for infinite-dimensional systems, even for linear ones.
Keywords: Nonlinear control systems; Infinite-dimensional systems; Practical stability; Non-coercive Lyapunov functions

Hojin Lee, Linh Thi Hoai Nguyen, Yasumasa Fujisaki,
Algebraic connectivity of network-of-networks having a graph product structure,
Systems & Control Letters,
Volume 104,
2017,
Pages 15-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117300476)
Abstract: In this paper, we present a method for finding the algebraic connectivity of network-of-networks having a graph product structure. The network consists of several homogeneous (identical) subsystems connected with each other according to an interconnection graph. We show that the algebraic connectivity can be calculated from properties of graphs corresponding to the subsystem and the interconnection. Furthermore, we indicate that the algebraic connectivity of the entire system does not exceed those of the subsystem and the interconnection.
Keywords: Network-of-networks; Graph product; Algebraic connectivity; Multi-agent systems

Thinh T. Doan, Alex Olshevsky,
Distributed resource allocation on dynamic networks in quadratic time,
Systems & Control Letters,
Volume 99,
2017,
Pages 57-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116301852)
Abstract: We consider the problem of allocating a fixed amount of resource among nodes in a network when each node suffers a cost which is a convex function of the amount of resource allocated to it. We propose a new deterministic and distributed protocol for this problem. Our main result is that the associated convergence time for the global objective scales quadratically in the number of nodes on any sequence of time-varying undirected graphs satisfying a long-term connectivity condition.
Keywords: Distributed optimization; Distributed resource allocation

Wen Kang, Emilia Fridman,
Sliding mode control of Schrödinger equation-ODE in the presence of unmatched disturbances,
Systems & Control Letters,
Volume 98,
2016,
Pages 65-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116301578)
Abstract: In this paper, we consider boundary stabilization for a cascade of Schrödinger equation-ODE system with both, matched and unmatched disturbances. The backstepping method is first applied to transform the system into an equivalent target system where the target system is input-to-state stable. To reject the matched disturbance, the sliding mode control (SMC) law is designed for the target system. The well-posedness of the closed-loop system is proved, and the reachability of the sliding manifold in finite time is justified by infinite-dimensional system theory. It is shown that the resulting closed-loop system is input-to-state stable. A Numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed-loop system by rejecting the matched disturbance.
Keywords: Distributed parameter systems; Schrödinger equation; Backstepping; Sliding mode control; Input-to-state stability

Xiaotao Liu, Yang Shi, Daniela Constantinescu,
Robust distributed model predictive control of constrained dynamically decoupled nonlinear systems: A contraction theory perspective,
Systems & Control Letters,
Volume 105,
2017,
Pages 84-91,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117300907)
Abstract: This paper considers the robust distributed model predictive control (MPC) of a group of dynamically decoupled nonlinear systems cooperating via the cost function subject to control constraints. Inspired by the contraction theory, we develop the robust distributed MPC scheme assuming that the dynamics of the cooperating systems satisfy the contraction property (they are contracting in a tube centered around a nominal state trajectory). Compared to conventional robust distributed MPC which uses the Lipschitz continuity property, the proposed method features the following aspects: (1) it can tolerate larger disturbances; and (2) it is feasible for a larger prediction horizon and could enlarge the feasible region accordingly. The paper evaluates the maximum disturbance which the nonlinear system can tolerate when controlled using the proposed method and derives sufficient conditions for the recursive feasibility of the optimization and for the practical stability of the closed-loop system. The effectiveness of the proposed method is illustrated using a simulation example.
Keywords: Distributed control; Model predictive control; Nonlinear systems; Continuous-time systems; Contracting dynamics; Optimization

Roger W. Brockett,
Thermodynamics with time: Exergy and passivity,
Systems & Control Letters,
Volume 101,
2017,
Pages 44-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116300755)
Abstract: In this paper we continue the exploration started in the joint paper Brockett and Willems (1978) with a view toward the further development of models for characterizing the limits on energy flow in mixed thermal–mechanical systems. We put the thermodynamic concept of exergy11The term exergy was coined by Zoran Rant in the 1950s. We choose to use it here instead of one of the other possible names such as available work, available energy, utilizable energy, etc. because it has a single precise meaning. Willems uses the term available energy in his major work on dissipative systems (Willems1972a, 1972b) but in a generic way. (available energy) in system theoretic terms and discuss its use as a storage function in the context of input–output models. In important cases the reachable sets for the systems considered here are not closed and of course this complicates any discussion of optimality. Only through the consideration of the closure of the reachable sets can the connection between optimal trajectories of dynamical systems and the basic results of classical thermodynamics be made tight.
Keywords: Optimal control; Stochastic control; Carnot cycle; Infinitesimal bracketing; Fluctuation–dissipation theorem; Free energy

Kyriakos G. Vamvoudakis,
Q-learning for continuous-time linear systems: A model-free infinite horizon optimal control approach,
Systems & Control Letters,
Volume 100,
2017,
Pages 14-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116301967)
Abstract: In this paper we propose an online Q-learning algorithm to solve the infinite-horizon optimal control problem of a linear time invariant system with completely uncertain/unknown dynamics. We first formulate the Q-function by using the Hamiltonian and the optimal cost. An integral reinforcement learning approach is used to develop an actor/critic approximator structure to estimate the parameters of the Q-function online while also guaranteeing closed-loop asymptotic stability and convergence to the optimal solution.
Keywords: Q-learning; Actor/critic approximators; Optimal control; Uncertain systems

F.D. Araruna, E. Fernández-Cara, S. Guerrero, M.C. Santos,
New results on the Stackelberg–Nash exact control of linear parabolic equations,
Systems & Control Letters,
Volume 104,
2017,
Pages 78-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117300622)
Abstract: This paper is concerned with Stackelberg–Nashstrategies to control parabolic equations. We have one control, the leader, that is responsible for a null controllability property; additionally, we have a couple of controls, called the followers, that provides a Nash equilibrium for two cost functionals. This is a classical situation in many fields of science and, in mathematics, leads to a lot of interesting questions and open problems and possesses many applications. In the main result, we prove the existence of a leader such that the corresponding controlled system is driven to zero. This way, we improve some questions that were left open in previous works.
Keywords: Controllability; Stackelberg–Nash strategies; Carleman inequalities

Brandon J. Wellman, Jesse B. Hoagg,
A flocking algorithm with individual agent destinations and without a centralized leader,
Systems & Control Letters,
Volume 102,
2017,
Pages 57-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117300105)
Abstract: We present a multi-agent control method that addresses the combined problem of flocking and destination seeking. The method is completely decentralized, that is, each agent’s controller relies on local sensing to determine the relative positions and velocities of nearby agents but does not rely on a centralized flock leader. Each agent has double-integrator dynamics and a potentially unique destination (i.e., position) that the agent must reach. We demonstrate that the flocking-and-destination-seeking control method accomplishes 2 objectives: (i) if an agent is far from its destination, then that agent flocks with nearby agents, and (ii) if an agent is close to its destination, then that agent approaches its destination. The flocking-and-destination-seeking algorithm is demonstrated with several numerical examples.
Keywords: Multi-agent systems; Flocking; Destination seeking

Rui Li, Yiguang Hong, Xingyuan Wang,
Nonlinear norm-observability and simulation of control systems,
Systems & Control Letters,
Volume 105,
2017,
Pages 14-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.011.
(http://www.sciencedirect.com/science/article/pii/S0167691117300865)
Abstract: The (bi)simulation relation has recently been attracting growing interest in the study of nonlinear control systems, in the hope that through such a relation, the behaviors and properties of a nonlinear system can be inferred from those of another system which is easier to handle. In this paper, we consider the propagation of the property of nonlinear norm-observability through a simulation relation. Given two control systems that are related by a graph simulation relation, we derive conditions under which the norm-observability of the simulating system implies the norm-observability of the simulated system. The obtained results are given in terms of set-valued functions. Several examples are included to illustrate various applications of our results.
Keywords: Norm-observability; Simulation relation; Nonlinear control system; Observability propagation


Editorial Board,
Systems & Control Letters,
Volume 100,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30021-X.
(http://www.sciencedirect.com/science/article/pii/S016769111730021X)

Jieqiong Wu, Xianzheng Zhu, Shugen Chai,
Controllability for one-dimensional nonlinear wave equations with degenerate damping,
Systems & Control Letters,
Volume 100,
2017,
Pages 66-72,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117300026)
Abstract: Internal exact controllability for the nonlinear wave equation in one space dimension ytt−yxx+g(y)yt=his studied, where g(⋅) is a nonnegative function. For the case, lim sup|s|→∞g(s)ln|s|<γ, we obtain the global exact controllability for the equation with Dirichlet boundary condition. The proof is based on the combination of fixed-point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t. For the case, g(s)=|s|, we only get a local exact controllability by means of Banach fixed-point theorem.
Keywords: Exact controllability; Wave equations; Degenerate damping

Xiaofan Wu, Mihailo R. Jovanović,
Sparsity-promoting optimal control of systems with symmetries, consensus and synchronization networks,
Systems & Control Letters,
Volume 103,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117300300)
Abstract: Optimal control problems in systems with symmetries and consensus/synchronization networks are characterized by structural constraints that arise either from the underlying group structure or the lack of absolute measurements for part of the state vector. Our objective is to design controller structures and resulting control strategies that utilize limited information exchange between subsystems in large-scale networks. To obtain controllers with low communication requirements, we seek solutions to regularized versions of the H2 optimal control problem. Non-smooth regularization terms are introduced to tradeoff network performance with sparsity of the feedback-gain matrix. In contrast to earlier results, our framework allows the state-space representations that are used to quantify the system’s performance and sparsity of the static output-feedback controller to be expressed in different sets of coordinates. We show how alternating direction method of multipliers can be leveraged to exploit the underlying structure and compute sparsity-promoting controllers. In particular, for spatially-invariant systems, the computational complexity of our algorithm scales linearly with the number of subsystems. We also identify a class of optimal control problems that can be cast as semidefinite programs and provide an example to illustrate our developments.
Keywords: Alternating direction method of multipliers; Consensus and synchronization networks; Distributed systems; Regularization; Sparsity-promoting optimal control; Spatially-invariant systems

O. Hernández-González, M. Farza, T. Ménard, B. Targui, M. M’Saad, C.M. Astorga-Zaragoza,
A cascade observer for a class of MIMO non uniformly observable systems with delayed sampled outputs,
Systems & Control Letters,
Volume 98,
2016,
Pages 86-96,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116301542)
Abstract: This paper investigates the observation problem for a class of MIMO non uniformly observable systems in the presence of sampled and delayed outputs. A high gain observer is first designed for the delay-free and continuous output measurement case. The observer gain involves the resolution of an appropriate Lyapunov differential equation allowing to show that the underlying observation error converges exponentially to zero under a well defined persistent excitation condition. This observer is then redesigned to cope with the output sampling process as well as the output delay thanks to an appropriate cascade structure composed of a set of dynamical subsystems. The first subsystem in the cascade is an impulsive continuous–discrete time observer which provides the estimation of the delayed state and each remaining subsystem in the cascade is a predictor which estimates the state over a small horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The exponential convergence to zero of the observation error related to the cascade observer is established for arbitrarily long delays provided that the maximum value of the sampling partition diameter is lower than a certain given bound. Simulations results are given to highlight the performance and the main properties of the proposed cascade observer.
Keywords: High gain observer; Non uniform observability; Cascade observer; Sampled outputs; Delayed outputs

Jan Willem Polderman,
Post unimodular transformations and isomorphisms for linear behaviors,
Systems & Control Letters,
Volume 101,
2017,
Pages 10-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115002522)
Abstract: In this paper we investigate to what extent right unimodular transformations induce isomorphisms between behaviors. The main result is that in order to constitute an isomorphism specific smoothness conditions need to be imposed.
Keywords: Controllability; Behavior; Smith form; Hautus test

K.M.D. Motchon, K.M. Pekpe, J.-P. Cassar,
Conditions for strict distinguishability of single-output nonlinear control-affine systems,
Systems & Control Letters,
Volume 105,
2017,
Pages 20-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117300816)
Abstract: Strict distinguishability is the property of two systems to generate identical output signals only for the zero control input and the zero initial state vector. The objective of this paper is to characterize this property for single-output nonlinear control-affine systems. In this context, we first introduce the indistinguishability zone of the systems. This zone represents the set of control inputs and initial state vectors that make the output signals of the systems indistinguishable. The explicit identification of the elements of this set is proposed in the paper. From this result, necessary and sufficient conditions for strict distinguishability are then established under suitable assumptions.
Keywords: Distinguishability; Nonlinear dynamical systems; Control-affine systems

Henrik Anfinsen, Ole Morten Aamo,
Adaptive stabilization of n+1 coupled linear hyperbolic systems with uncertain boundary parameters using boundary sensing,
Systems & Control Letters,
Volume 99,
2017,
Pages 72-84,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116301931)
Abstract: We design an adaptive control law stabilizing a class of systems of the form of n+1 linear partial differential equations (PDEs) of the hyperbolic type from boundary sensing only. We do this by combining a recently derived observer based on swapping design, with a backstepping-based adaptive control law with time-varying gains. Boundedness of all signals in the closed loop system and asymptotic convergence to zero pointwise in space for the system states are proved. The theory is demonstrated in a simulation.
Keywords: Distributed systems; Adaptive control; Backstepping


Editorial Board,
Systems & Control Letters,
Volume 104,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30093-2.
(http://www.sciencedirect.com/science/article/pii/S0167691117300932)

Daniel E. Miller,
A parameter adaptive controller which provides exponential stability: The first order case,
Systems & Control Letters,
Volume 103,
2017,
Pages 23-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.009.
(http://www.sciencedirect.com/science/article/pii/S0167691117300415)
Abstract: Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however, neither exponential stabilization nor a bounded noise gain is typically proven. Here we consider the first order case and prove that if the original, ideal, projection algorithm is used in the estimation process (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set), then it guarantees linear-like convolution bounds on the closed loop behaviour, which implies exponential stability and a bounded noise gain, as well an easily proven tolerance to unmodelled dynamics and plant parameter variation.
Keywords: Adaptive control; Projection algorithm; Projection; Exponential stability; Bounded gain

Shan Ma, Ian R. Petersen, Matthew J. Woolley,
Linear quantum systems with diagonal passive Hamiltonian and a single dissipative channel,
Systems & Control Letters,
Volume 99,
2017,
Pages 64-71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.013.
(http://www.sciencedirect.com/science/article/pii/S016769111630192X)
Abstract: Given any covariance matrix corresponding to a so-called pure Gaussian state, a linear quantum system can be designed to achieve the assigned covariance matrix. In most cases, however, one might obtain a system that is difficult to realize in practice. In this paper, we restrict our attention to a special class of linear quantum systems, i.e., systems with diagonal passive Hamiltonian and a single dissipative channel. The practical implementation of such a system would be relatively simple. We then parametrize the class of pure Gaussian state covariance matrices that can be achieved by this particular type of linear quantum system.
Keywords: Linear quantum system; Covariance assignment; Pure Gaussian state; Diagonal Hamiltonian; Passive Hamiltonian; Single dissipative channel

Feng Xiao, Tongwen Chen, Huijun Gao,
Consensus in time-delayed multi-agent systems with quantized dwell times,
Systems & Control Letters,
Volume 104,
2017,
Pages 59-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.012.
(http://www.sciencedirect.com/science/article/pii/S0167691117300658)
Abstract: This paper investigates the effects of quantized dwell times in solving consensus problems in time-delayed multi-agent systems with the asynchronous property of unpredictable quantization jumps in inter-agent communications. The quantized dwell times can be introduced on purpose or be inherent from quantizing devices. They beneficially avoid undesirable fast chattering of quantizers’ outputs and mathematical difficulties in convergence analysis. The main result shows that the largest eigenvalue of the interaction graph Laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time-varying transmission delays. Simulations are presented to show the effectiveness of the main result.
Keywords: Multi-agent systems; Quantized consensus; Time delays; Dwell times

Johan Markdahl, Jens Hoppe, Lin Wang, Xiaoming Hu,
A geodesic feedback law to decouple the full and reduced attitude,
Systems & Control Letters,
Volume 102,
2017,
Pages 32-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117300099)
Abstract: This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n−1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.
Keywords: Attitude control; Reduced attitude; Geodesics; Exact solutions; Special orthogonal group

Xinglong Niu, Yungang Liu, Yongchao Man,
Consensus via time-varying feedback for uncertain nonlinear multi-agent systems with rather coarse input disturbances,
Systems & Control Letters,
Volume 105,
2017,
Pages 70-77,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117300890)
Abstract: This paper is concerned with the leader-following consensus for a class of uncertain nonlinear multi-agent systems (NMASs) with rather coarse input disturbances, unknown control coefficients and unknown Lipschitz rate. The essential unknowns render the existing compensation strategies inapplicable and motivate us to explore a new one. First, a time-varying strategy is developed to compensate the essential unknowns, where a suitable design function of time is introduced so that the unknowns can be overtaken by the design function as time increases. Then, distributed time-varying consensus protocols are designed and the leader-following consensus is achieved. When essential time-variations exist, the designed consensus protocols are still valid if the involved design function of time is replaced by a new one. Two examples are given to illustrate the effectiveness of the proposed protocols.
Keywords: Nonlinear multi-agent systems; Rather coarse input disturbances; Unknown control coefficients; Unknown Lipschitz rate; Leader-following consensus; Time-varying feedback

Jian Wang,
Quantizer design for asymptotic stability of quantized linear systems with saturations,
Systems & Control Letters,
Volume 104,
2017,
Pages 95-103,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117300774)
Abstract: This paper considers continuous linear systems involving input saturations and quantized control laws. Based on spherical polar coordinates, a quantizer of infinite data rate is proposed with a definite relation between the quantized data and the corresponding quantization error. By the proposed quantizer, state feedback controllers are designed for input quantization case and state quantization case, respectively, to achieve both local asymptotic stability and larger stability regions of the systems. Further, a quantizer of finite data rate is proposed for the same problem.
Keywords: Quantized control; Saturation; Stability regions; Asymptotic stability

Yijing Xie, Zongli Lin,
Global optimal consensus for multi-agent systems with bounded controls,
Systems & Control Letters,
Volume 102,
2017,
Pages 104-111,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117300257)
Abstract: This paper studies the global optimal consensus problem for a multi-agent system with bounded controls. Each agent has its own objective function which is known only to itself. We focus on two multi-agent systems, the single integrator multi-agent system and the double-integrator multi-agent system. For each of these two multi-agent systems, we construct, for each agent, a bounded local control protocol that uses the information accessible to it through the communication topology underlying the multi-agent system and information of its own objective function. It is shown that these control protocols together achieve global optimal consensus for the multi-agent system, that is, all agents reaching consensus at a state that minimizes the sum of the objective functions of all agents as long as the communication topology is strongly connected and detailed balanced. Simulation results are given to illustrate the theoretical results.
Keywords: Multi-agent systems; Bounded control; Distributed optimization; Consensus; Optimal consensus

Myung-Gon Yoon,
Consensus of adaptive multi-agent systems,
Systems & Control Letters,
Volume 102,
2017,
Pages 9-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.006.
(http://www.sciencedirect.com/science/article/pii/S0167691117300014)
Abstract: This paper studies a leader–follower consensus problem for a multi-agent system composed of identical adaptive agents. We propose a distributed adaptive protocol with which a successful consensus is guaranteed if inter-agent communication is purely bidirectional. When unidirectional communication exists, the closed loop census system employing the proposed protocol is locally stable near a consensus state. A numerical example is presented to illustrate our theoretical findings and properties of our adaptive consensus system.
Keywords: Consensus; Adaptive; Leader–follower; Model identification

S.C. Jugade, Debasattam Pal, Rachel K. Kalaimani, Madhu N. Belur,
Fast modes in the set of minimal dissipation trajectories,
Systems & Control Letters,
Volume 101,
2017,
Pages 28-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116000384)
Abstract: In this paper, we study the set of trajectories satisfying both a given LTI system’s laws and also laws of the corresponding ‘adjoint’ system: in other words, trajectories in the intersection of the system’s behavior and that of the adjoint system. This intersection has important system theoretic significance: for example, it is known that the trajectories in this intersection are the ones with minimal ‘dissipation’. Underlying the notion of adjoint is that of a power supply: it is with respect to this supply rate that the trajectories in the intersection are known to be ‘stationary’. In this paper, we deal with half-line solutions to the differential equations governing both the system and its adjoint. Analysis of half-line solutions plays a central role for example in initial value problems and in well-posedness studies of an interconnection. We interpret the set of half-line trajectories allowed by a system and its adjoint as an interconnection of these two systems, and thus address issues about well-posedness/ill-posedness of the interconnection. We formulate necessary and sufficient conditions for this intersection to be autonomous. For the case of an ill-posed interconnection and resulting autonomous system, we derive conditions for existence of initial conditions that lead to impulsive solutions in the states of the system. We link our conditions with the strongly reachable and weakly unobservable subspaces of a state space system. We show that absence of impulsive initial conditions is equivalent to the well-known subspace iteration algorithms for these subspaces converging in one step.
Keywords: Inadmissible initial conditions; Zeros at infinity; Ill-posed interconnection; Strongly reachable subspace; Weakly unobservable subspace; Impulse observability

Xiaoying Zhang, Hongyinping Feng, Shugen Chai,
Performance output exponential tracking for a wave equation with a general boundary disturbance,
Systems & Control Letters,
Volume 98,
2016,
Pages 79-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116301554)
Abstract: In this paper, we consider performance output tracking for a wave equation with a general boundary disturbance. The control and the disturbance are unmatched. Different from the existing results, the hidden regularity, instead of the high gain or variable structure, is utilized in the adaptive servomechanism design. As a result, we are able to cope with more complicated and general disturbances. Moreover, the performance output can track the reference signal exponentially, and at the same time, all the states of the subsystems involved are uniformly bounded. More specially, the overall closed-loop system is exponentially stable when the disturbance and reference are disconnected to the system. The numerical simulations are presented to illustrate the effect of the proposed scheme.
Keywords: Disturbance; Hidden regularity; Performance output tracking; Wave equation


Editorial Board,
Systems & Control Letters,
Volume 99,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30200-6.
(http://www.sciencedirect.com/science/article/pii/S0167691116302006)

Guangchen Zhang, Harry L. Trentelman, Weiqun Wang, Jingbo Gao,
Input–output finite-region stability and stabilization for discrete 2-D Fornasini–Marchesini models,
Systems & Control Letters,
Volume 99,
2017,
Pages 9-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116301670)
Abstract: This paper establishes input–output finite-region stability (I–O FRS) and stabilization analysis methods to investigate the transient behavior of output signals for discrete two-dimensional (2-D) Fornasini–Marchesini (FM) models. For 2-D systems with two classes of input signals, by building special recursive formulas, sufficient I–O FRS conditions are formulated in terms of solvability of linear matrix inequalities (LMIs). Furthermore, aiming at designing static state feedback controllers, I–O finite-region stabilization issues are analyzed for the corresponding 2-D systems and sufficient conditions are reported to guarantee I–O FRS of the closed-loop systems. To conclude the paper, we provide some numerical examples to confirm the validity of the proposed methods.
Keywords: Input–output finite-region stability; Input–output finite-region stabilization; 2-D Fornasini–Marchesini models; State feedback controllers

Qi Wang, Junjie Fu, Jinzhi Wang,
Fully distributed containment control of high-order multi-agent systems with nonlinear dynamics,
Systems & Control Letters,
Volume 99,
2017,
Pages 33-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116301827)
Abstract: In this paper, distributed containment control problems for high-order multi-agent systems with nonlinear dynamics are investigated under directed communication topology. The states of the leaders are only available to a subset of the followers and the inputs of the leaders are possibly nonzero and time varying. Distributed adaptive nonlinear protocol is proposed based only on the relative state information, under which the states of the followers converge to the dynamic convex hull spanned by those of the leaders. As the special case with only one dynamic leader, leader–follower consensus problem is also solved with the proposed protocol. The adaptive protocol here is independent of the eigenvalues of the Laplacian matrix, which means the protocol can be implemented by each agent in a fully distributed fashion. A simulation example is provided to illustrate the theoretical results.
Keywords: High-order multi-agent systems; Nonlinear dynamics; Adaptive containment control; Directed graph

A.R.F. Everts, M.K. Camlibel,
When is a linear multi-modal system disturbance decoupled?,
Systems & Control Letters,
Volume 101,
2017,
Pages 50-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116300457)
Abstract: In this paper we study the question under which conditions a linear multi-modal system is disturbance decoupled. We establish necessary and sufficient geometric conditions from which the existing results on switched linear systems and conewise linear systems can be recovered as special cases. Also, we apply these conditions to a class of linear complementarity systems in order to obtain a more crisp characterization.
Keywords: Disturbance decoupling; Hybrid systems; Piecewise-affine systems; Conewise linear systems; Switched systems; Linear complementarity systems

Milan Korda, Didier Henrion, Colin N. Jones,
Convergence rates of moment-sum-of-squares hierarchies for optimal control problems,
Systems & Control Letters,
Volume 100,
2017,
Pages 1-5,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.010.
(http://www.sciencedirect.com/science/article/pii/S016769111630189X)
Abstract: We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is O(1∕loglogd). We treat in detail the continuous-time infinite-horizon discounted problem and describe in brief how the same rate can be obtained for the finite-horizon continuous-time problem and for the discrete-time counterparts of both problems.
Keywords: Optimal control; Moment relaxations; Polynomial sums of squares; Convergence rate; Semidefinite programming; Approximation theory

Dan Martinec, Ivo Herman, Michael Šebek,
A travelling wave approach to a multi-agent system with a path-graph topology,
Systems & Control Letters,
Volume 99,
2017,
Pages 90-98,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116301943)
Abstract: The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the ‘local’ perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents create a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system.
Keywords: Multi-agent system; Travelling waves; Wave transfer function; Path graph; Irrational transfer function

Shiqi Zheng,
Robust stability of fractional order system with general interval uncertainties,
Systems & Control Letters,
Volume 99,
2017,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116301669)
Abstract: This paper focuses on the analysis of robust stability of fractional order system with general interval uncertainties. The concept of general interval uncertainties means that the interval uncertainties exist both in the coefficients and orders of the fractional order system. Necessary and sufficient conditions are proposed to check the robust stability of general interval fractional order system. According to the proposed stability criterion, it is interesting to find that the Edge Theorem, which was initially proposed for integer order system, cannot be directly extended to test the stability of fractional order system with general interval uncertainties. Examples are followed to verify the validity of the proposed method.
Keywords: Fractional order control system; Interval uncertainty; Robust stability

Alán Tapia, Miguel Bernal, Leonid Fridman,
Nonlinear sliding mode control design: An LMI approach,
Systems & Control Letters,
Volume 104,
2017,
Pages 38-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.011.
(http://www.sciencedirect.com/science/article/pii/S0167691117300646)
Abstract: This paper presents a novel nonlinear sliding mode control methodology for systems with both matched and unmatched perturbations (including parametric uncertainties). Instead of traditional approaches where uncertainties and nonlinearities are coped with via linear nominal models and linear sliding surfaces, the proposed approach incorporates exact convex expressions to represent both the nonlinear surface and the system, thus allowing a significant chattering reduction. Moreover, thanks to the convex form of the nonlinear nominal model, when combined with the direct Lyapunov method, it leads to linear matrix inequalities, which are efficiently solved via convex optimization techniques. Illustrative examples are provided.
Keywords: Nonlinear sliding surface; Convex models; Linear matrix inequalities

P. Pepe, I. Karafyllis, Z.P. Jiang,
Lyapunov–Krasovskii characterization of the input-to-state stability for neutral systems in Hale’s form,
Systems & Control Letters,
Volume 102,
2017,
Pages 48-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.01.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117300129)
Abstract: The primary contribution of the paper is to show that the Lyapunov–Krasovskii conditions available in the literature, for checking the input-to-state stability property of systems described by neutral functional differential equations in Hale’s form, are also necessary. It is shown that the Lyapunov–Krasovskii conditions available in the literature are equivalent to the input-to-state stability property, for an enlarged class of neutral systems. Finally, a novel necessary and sufficient condition for the input-to-state stability property is provided.
Keywords: Neutral functional differential equations; Converse Lyapunov–Krasovskii theorems; Input-to-state stability; Time delays

Bao Wang, Quanxin Zhu,
Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems,
Systems & Control Letters,
Volume 105,
2017,
Pages 55-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.05.002.
(http://www.sciencedirect.com/science/article/pii/S0167691117300889)
Abstract: This paper discusses the asymptotic stability of Markov switched stochastic differential equations. By using the method of multiple Lyapunov functions, we provide sufficient conditions for stochastic asymptotic stability of Markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple Lyapunov functions and the stationary distribution of Markovian switching process. Particularly, our results include some existing results as special cases and improve some results in the literature. Two examples are given to illustrate the effectiveness of the obtained results.
Keywords: Markov switched stochastic differential equation; Stochastically asymptotically stable in the large; Multiple Lyapunov function; Unstable subsystem

Vojtech Veselý, Adrian Ilka,
Generalized robust gain-scheduled PID controller design for affine LPV systems with polytopic uncertainty,
Systems & Control Letters,
Volume 105,
2017,
Pages 6-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117300804)
Abstract: In the paper a generalized guaranteed cost output-feedback robust gain-scheduled PID controller synthesis is presented for affine linear parameter-varying systems under polytopic model uncertainty. The controller synthesis is generalized in a sense that it covers robust, robust gain-scheduled, and robust switched (with arbitrary switching algorithm) PID controller design. The proposed centralized/decentralized controller method is based on Bellman–Lyapunovequation, guaranteed cost, and parameter-dependent quadratic stability. The proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities (BMI) which can efficiently be solved or further linearized. As the main result, the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples.
Keywords: Robust controller; Gain-scheduled controller; Switched controller; Parameter-dependent Lyapunov function; Bellman–Lyapunov equation

Pengpeng Zhang, Tengfei Liu, Zhong-Ping Jiang,
Input-to-state stabilization of nonlinear discrete-time systems with event-triggered controllers,
Systems & Control Letters,
Volume 103,
2017,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.012.
(http://www.sciencedirect.com/science/article/pii/S0167691117300440)
Abstract: This paper studies an event-triggered control problem of nonlinear discrete-time systems in the presence of external disturbances. In particular, we focus on the practically interesting situation where the controller update at step k is determined by the feedback information x(k−1) measured at step k−1. The presence of external disturbance makes it hard to predict the magnitude of x(k) based on x(k−1) and then to design a desired event-triggering data transmission mechanism. In this paper, refined tools of input-to-state stability (ISS) and the nonlinear small-gain theorem are developed to estimate the influence of external disturbances, before an ISS-induced design is proposed to solve the problem. The proposed solution leads to a new event-triggering data transmission mechanism, which drastically differs from the existing event-triggered control results.
Keywords: Event-triggered control; Nonlinear discrete-time systems; Input-to-state stabilization

Víctor Ayala, Adriano Da Silva,
A semigroup associated to a linear control system on a Lie group,
Systems & Control Letters,
Volume 98,
2016,
Pages 33-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.021.
(http://www.sciencedirect.com/science/article/pii/S0167691116301487)
Abstract: Let us consider a linear control system Σ on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object SΣ to Σ which turns out to be a semigroup, allowing the use of the semigroup machinery to approach Σ. In particular, we obtain some controllability results.
Keywords: Linear control systems; Semigroups; Controllability; Lie groups

Ankush Chakrabarty, Raid Ayoub, Stanisław H. Żak, Shreyas Sundaram,
Delayed unknown input observers for discrete-time linear systems with guaranteed performance,
Systems & Control Letters,
Volume 103,
2017,
Pages 9-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691117300282)
Abstract: In this paper, we propose a state and unknown input observer for discrete-time linear systems with bounded unknown inputs and measurement disturbances. The design procedure is formulated using a set of linear matrix inequalities, and leverages delayed (or fixed-lag) estimates. The observer error states and/or user-defined performance outputs are guaranteed to operate at certain performance bounds. Furthermore, by employing sufficiently large delays, the observer is guaranteed to provide exact asymptotic state and input estimates for minimum-phase systems. We demonstrate, via numerical examples, that the proposed observer can be used for a wider class of systems than those satisfying matching conditions.
Keywords: Unknown input observer; Attack detection; Linear matrix inequalities; Delayed estimation; 
               ℓ∞ observer

Lixian Zhang, Wei Xing Zheng, Huijun Gao,
H∞ model reduction of switched LPV systems via semi-time-varying reduced-order model,
Systems & Control Letters,
Volume 98,
2016,
Pages 25-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116301517)
Abstract: This paper investigates the problem of model reduction for a class of switched linear parameter varying (LPV) systems with persistent dwell-time (PDT) switching property. The PDT switching generalizes the dwell-time and average dwell-time switching that are commonly concerned in the existing literature. To reduce the original high-order model with less conservatism, the constructed reduced-order model is both parameterized and semi-time-varying such that the model error system is uniformly stable over the PDT switching and guarantees an error performance in H∞ sense. A numerical example is used to verify the validity and advantage of the theoretical results.
Keywords: Linear parameter varying (LPV) systems; Model reduction; Persistent dwell-time switching; Semi-time-varying

Amir Baniamerian, Nader Meskin, Khashayar Khorasani,
Fault detection and isolation of two-dimensional (2D) systems,
Systems & Control Letters,
Volume 99,
2017,
Pages 25-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116301876)
Abstract: In this work, we develop a novel fault detection and isolation (FDI) scheme for discrete-time two-dimensional (2D) systems that are represented by the Fornasini–Marchesini model II (FMII). This is accomplished by generalizing the basic invariant subspaces including unobservable, conditioned invariant and unobservability subspaces of 1D systems to 2D models. These extensions have been achieved and facilitated by representing a 2D model as an infinite dimensional (Inf-D) system on a Banach vector space, and by particularly constructing algorithms that compute these subspaces in a finite and known number of steps. By utilizing the introduced subspaces, the FDI problem is formulated and necessary and sufficient conditions for its solvability are provided. Sufficient conditions for solvability of the FDI problem for 2D systems using both deadbeat and LMI-based filters have also been developed. Moreover, the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the currently available 2D geometric methods in the literature.
Keywords: Two-dimensional (2D) systems; Fornasini–Marchesini model; Infinite-dimensional (Inf-D) systems; Fault detection and isolation (FDI); Geometric approach

Martin Redmann, Peter Benner,
An H2-type error bound for balancing-related model order reduction of linear systems with Lévy noise,
Systems & Control Letters,
Volume 105,
2017,
Pages 1-5,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117300798)
Abstract: To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear differential equations of high order. To reduce the high dimension for practical computations, model order reduction is frequently used. Balanced truncation (BT) is a well-known technique from deterministic control theory and it was already extended for controlled linear systems with Lévy noise. Recently, a new ansatz was investigated which provides an alternative way to generalize BT for stochastic systems. There, the question of the existence of an H2-error bound was asked which we answer in this paper. We discuss how this bound can be computed practically and how to use it to find a suitable reduced order dimension.
Keywords: Model reduction; Stochastic control; Stochastic systems; Stochastic jump processes

Junwei Wang, Kairui Chen, Frank L. Lewis,
Coordination of multi-agent systems on interacting physical and communication topologies,
Systems & Control Letters,
Volume 100,
2017,
Pages 56-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.12.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117300038)
Abstract: A new framework is given for coordination of multi-agent systems that are interconnected by a physical coupling digraph. The edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions. On top of the physical graph, distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph. The physical and communication digraphs are generally different and the combination of these two graphs forms a cyber-physical system. The interactions between physical and communication graphs are the focus of this paper. We consider different interactions between two graphs, including the case when their pinned Laplacian commutes, the case of the communication graph with diagonalizable pinned Laplacian, and the case of two general graphs. Moreover, within each graph, the relations between the agents can be either collaborative or antagonistic. To capture this, the theory of bipartite consensus is used. Coordination protocols for different cases are designed that are distributed with respect to the communication graph, and overcome the detrimental effects of the signed physical graph. The proposed control methods are illustrated by simulation examples.
Keywords: Consensus; Bipartite consensus; Multi-agent systems; Two interaction graphs

Georges Bastin, Jean-Michel Coron,
A quadratic Lyapunov function for hyperbolic density–velocity systems with nonuniform steady states,
Systems & Control Letters,
Volume 104,
2017,
Pages 66-71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.03.013.
(http://www.sciencedirect.com/science/article/pii/S016769111730066X)
Abstract: A new explicit Lyapunov function allows to study the exponential stability for a class of physical ‘2 by 2’ hyperbolic systems with nonuniform steady states. In fluid dynamics, this class of systems involves isentropic Euler equations and Saint-Venant equations. The proposed quadratic Lyapunov function allows to analyze the local exponential stability of the system equilibria for suitable dissipative Dirichlet boundary conditions without additional conditions on the system parameters.
Keywords: Stability; Lyapunov; Hyperbolic; Euler equation; Partial differential equation

Yang Liu, Zidong Wang, Xiao He, D.H. Zhou,
Finite-horizon quantized H∞ filter design for a class of time-varying systems under event-triggered transmissions,
Systems & Control Letters,
Volume 103,
2017,
Pages 38-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.011.
(http://www.sciencedirect.com/science/article/pii/S0167691117300439)
Abstract: This paper is concerned with the finite-horizon quantized H∞ filter design problem for a class of time-varying systems with quantization effects and event-triggered measurement transmissions. A componentwise event-triggered transmission strategy is put forward to reduce the unnecessary communication burden for the purpose of energy efficiency. The transmitted measurements triggered according to prespecified events are quantized by a logarithmic quantizer. Special attention is paid to the design of the filter such that a prescribed H∞ performance can be guaranteed over a given finite horizon in the presence of nonlinearities, quantization effects and event-triggered transmissions. Two sets of Riccati difference equations are introduced to ensure the H∞ estimation performance of the designed filter. The filter design algorithm is recursive and thus suitable for online computation. A simulation example is illustrated to show the effectiveness of the proposed algorithm applied to the fault detection problem.
Keywords: Nonlinear systems; Event-triggered transmission; Quantization; Recursive Riccati equations

Juliang Yin, Suiyang Khoo, Zhihong Man,
Finite-time stability theorems of homogeneous stochastic nonlinear systems,
Systems & Control Letters,
Volume 100,
2017,
Pages 6-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.012.
(http://www.sciencedirect.com/science/article/pii/S0167691116301918)
Abstract: The purpose of this paper is to study finite-time stability of a class of homogeneous stochastic nonlinear systems modeled by stochastic differential equations. An existence result of weak solutions for stochastic differential equations with continuous coefficients is derived as a preparation for discussing stochastic nonlinear systems. Then a generalization of finite-time stochastic stability theorem is given. By using some properties of homogeneous functions and homogeneous vector fields, it is proved that a homogeneous stochastic nonlinear system is finite-time stable if its coefficients have negative degrees of homogeneity, and there exists a sufficiently smooth and homogeneous Lyapunov function such that the infinitesimal generator of the stochastic system acting on it is negative definite. In the case when the drift coefficient of a stochastic system is homogeneous and has a negative degree of homogeneity, it can be shown that the stochastic system is also finite-time stable under appropriate conditions. Two examples are provided as illustrations.
Keywords: Finite-time stochastic stability; Stochastic nonlinear systems; Homogeneity; Homogeneous Lyapunov functions

Yueqian Liang, Yingmin Jia,
Tangent vector field approach for curved path following with input saturation,
Systems & Control Letters,
Volume 104,
2017,
Pages 49-58,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.001.
(http://www.sciencedirect.com/science/article/pii/S0167691117300671)
Abstract: Path following is an indispensable function for autonomous vehicles. Desired paths may be of arbitrary shape, not just the mostly investigated straight lines and circles. This paper addresses the path following problem of arbitrary twice differentiable curves using vector-field-based approach. A tangent vector field is constructed through coordinate transformation, and a sufficient condition for its feasibility concerning the input saturation is given out. A saturated turning velocity controller is designed and its Lyapunov stability is discussed in detail. Numerical simulation results show us that the path following performance of the proposed approach is comparable with that of the literature while involving 5 less parameters to be set.
Keywords: Path following; Autonomous vehicle; Guidance vector field; Lyapunov stability; Input saturation

Paolo Rapisarda, Harry L. Trentelman,
Preface: Second Volume of The Special Issue Dedicated to Jan C. Willems,
Systems & Control Letters,
Volume 101,
2017,
Page 1,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.008.
(http://www.sciencedirect.com/science/article/pii/S0167691117300312)

Arjan van der Schaft,
Modeling of physical network systems,
Systems & Control Letters,
Volume 101,
2017,
Pages 21-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115001814)
Abstract: Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and the extension to k-complexes is indicated. Physical distribution networks often involve a non-symmetric Laplacian matrix. It is shown how, in case the connected components of the graph are strongly connected, such systems can be converted into a form with balanced Laplacian matrix by constructive use of Kirchhoff’s Matrix Tree theorem, giving rise to a port-Hamiltonian description. Application to the dual case of asymmetric consensus algorithms is given. Finally it is shown how the minimal storage function for physical network systems with controlled flows can be explicitly computed.
Keywords: Physical network; Laplacian matrix; Matrix Tree theorem; Port-Hamiltonian system; Available storage

Maryam Babazadeh, Amin Nobakhti,
Robust controllability assessment via semi-definite programming,
Systems & Control Letters,
Volume 98,
2016,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116301499)
Abstract: This paper presents a new framework for systematic assessment of the controllability of uncertain linear time-invariant (LTI) systems. The objective is to evaluate controllability of an uncertain system with norm-bounded perturbation over the entire uncertain region. The method is based on a singular-value minimization problem, over the entire complex plane. To solve the problem, first, a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane, and to verify the controllability of directed and undirected networks in a single step. Secondly, the results are utilized to formulate the problem as two Lyapunov-based linear matrix inequalities (LMIs) for undirected networks, and four LMIs, for directed ones. The proposed approach is subsequently extended to evaluate the maximum guaranteed distance to uncontrollability of a system through a quasi-convex optimization problem whose solution is guaranteed to be globally optimal. By duality, analogous results are established for robust observability of directed and undirected networks. The proposed framework is implemented efficiently using LMI tools, and provides a fast and reliable tool for the assessment of robust controllability (and by duality, robust observability). It is also extendable to robust control system design problems such as control node selection for uncertain systems.
Keywords: Directed network; Undirected network; Semi-definite programming (SDP); Controllability; Observability; Norm-bounded uncertainty

Timothy H. Hughes, Malcolm C. Smith,
Controllability of linear passive network behaviors,
Systems & Control Letters,
Volume 101,
2017,
Pages 58-66,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115001899)
Abstract: Classical RLC realization procedures (e.g. Bott–Duffin) result in networks with uncontrollable driving-point behaviors. With this motivation, we use the behavioral framework of Jan Willems to provide a rigorous analysis of RLC networks and passive behaviors. We show that the driving-point behavior of a general RLC network is stabilizable, and controllable if the network contains only two types of elements. In contrast, we show that the full behavior of the RLC network need not be stabilizable, but is marginally stabilizable. These results allow us to formalize the phasor approach to RLC networks using the notion of sinusoidal trajectories, and to address an assumption of conventional phasor analysis. Finally, we show that any passive behavior with a hybrid representation is stabilizable. This paper relies substantially on the fundamental work of our late friend and colleague Jan Willems to whom the paper is dedicated.
Keywords: Behaviors; Electric circuits; Mechanical networks; Passivity; Controllability; Stabilizability

Quanxin Zhu, Feng Jiang, Hui Wang, Bao Wang,
Comment on “Stability analysis of stochastic differential equations with Markovian switching” [Systems & Control Letters 61 (2012) 1209–1214],
Systems & Control Letters,
Volume 102,
2017,
Pages 102-103,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691117300270)
Abstract: The reader will have noticed that the proof of Lemma 3.1 in Zhu et al. (2012) is obviously wrong. The same mistake appears in the proof of Theorem 3.1 in Zhu et al. (2015). In this note, we give a corrected proof.
Keywords: Stochastic differential equation; Markovian switching; Time varying delay

Paolo Forni, David Angeli,
Input-to-state stability for cascade systems with multiple invariant sets,
Systems & Control Letters,
Volume 98,
2016,
Pages 97-110,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301530)
Abstract: In a recent paper Angeli and Efimov (2015), the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems and we characterize the finest possible decomposition of its invariant set for three different scenarios: 1. the driving system exhibits multistability (convergence to fixed points only); 2. the driving system exhibits multi-almost periodicity (convergence to fixed points as well as periodic and almost-periodic orbits) and the driven system is assumed to be incremental ISS; 3. the driving system exhibits multiperiodicity (convergence to fixed points and periodic orbits) whereas the driven system is ISS in the sense of Angeli and Efimov (2015). Furthermore, we provide marginal results on the backward/forward asymptotic behavior of incremental ISS systems and on the response of a contractive system under asymptotically almost-periodic forcing. Three examples illustrate the potentiality of the proposed framework.
Keywords: Input-to-state stability; Lyapunov methods; Interconnections

Xiuxiang Zhou,
Integral-type approximate controllability of linear parabolic integro-differential equations,
Systems & Control Letters,
Volume 105,
2017,
Pages 44-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.007.
(http://www.sciencedirect.com/science/article/pii/S0167691117300828)
Abstract: This paper addresses the study of the integral-type approximate controllability of linear parabolic integro-differential equations. This new controllability is defined by imposing some additional integral-type constraints on the usual approximate controllability and therefore, can be used to keep the state close to the target. The paper is concerned with a special choice of integral kernels, which are multiples of the same exponential function. We reduce the problem of new controllability to the obtention of a unique continuation property for the suitable adjoint system.
Keywords: Parabolic integro-differential equations; Integral-type approximate controllability; Unique continuation property

T.M. Maupong, P. Rapisarda,
Data-driven control: A behavioral approach,
Systems & Control Letters,
Volume 101,
2017,
Pages 37-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116300317)
Abstract: In this work, we study the design of a controller using system data. We present three data-driven approaches based on the notion of control as interconnection. In the first approach, we use both the data and representations to compute control variable trajectories that impose a prescribed path on the to-be-controlled variables. The second method is completely data-driven and we prove sufficient conditions for determining a controller directly from data. Finally, we show how to determine a controller directly from data in the case where the control and to-be-controlled variables coincide.
Keywords: Data-driven control; Behavioral approach; Interconnection; Annihilators

Jung-Min Yang,
Static feedback control of switched asynchronous sequential machines,
Systems & Control Letters,
Volume 99,
2017,
Pages 40-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.11.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116301888)
Abstract: This paper presents model matching of switched asynchronous sequential machines (ASMs) using static feedback control. Comprised of a number of submachines, the switched ASM changes its present mode according to the switching signal generated by the controller. Not only the state transitions in each submachine but also the switching operations over different submachines are carried out in an asynchronous mechanism. The control goal is to make the stable-state behavior of the closed-loop system exhibit the same input/state characteristics as a given reference model. In particular, we focus on designing a static controller, which consists of only logic gates with no memory elements, in order to minimize the controller size. The study of a synthetic example is provided to illustrate the existence condition for a feedback controller and its construction algorithm.
Keywords: Asynchronous sequential machines (ASMs); Switched systems; Corrective control; Static controllers


Editorial Board,
Systems & Control Letters,
Volume 105,
2017,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(17)30110-X.
(http://www.sciencedirect.com/science/article/pii/S016769111730110X)

A.Yu. Aleksandrov, E.B. Aleksandrova,
Convergence conditions for some classes of nonlinear systems,
Systems & Control Letters,
Volume 104,
2017,
Pages 72-77,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.04.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117300786)
Abstract: Systems of differential equations with nonlinearities of a sector type and almost periodic perturbations are studied. With the aid of the Lyapunov direct method, conditions are found under which the considered systems admit globally asymptotically stable almost periodic solutions. Moreover, it is shown that the proposed approach permits us to derive new convergence conditions for some models of neural networks and generalized Lotka–Volterra models of population dynamics. An example is presented to demonstrate the effectiveness of the obtained results.
Keywords: Nonlinear nonstationary systems; Almost periodic oscillations; Asymptotic stability; Convergence; Lyapunov functions; Population dynamics

Qingbin Gao, Nejat Olgac,
Stability analysis for LTI systems with multiple time delays using the bounds of its imaginary spectra,
Systems & Control Letters,
Volume 102,
2017,
Pages 112-118,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691117300269)
Abstract: The stability of linear time invariant (LTI) systems with multiple independent time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. Any delay composition that results in an imaginary characteristic root lies either on a small number of kernel hypersurfaces (KH) or their infinitely many offspring hypersurfaces (OH). The complete description of KH is the only prerequisite for the CTCR-based stability assessment procedure. As the number of delays increases, however, the determination of these KH becomes computationally costly. Instead, we present a practical procedure to extract the 2-D cross-sections of the KH set in the domain of the two arbitrarily selected delays. First, we determine the exact upper and lower bounds of the imaginary spectra in this 2-D cross-section of interest. This process starts with a half-angle tangent representation of the characteristic equation followed by the Dixon resultant operation. Based on the full knowledge of KH, the CTCR paradigm creates the complete stability map in the domain of these two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study.
Keywords: Dixon resultant; CTCR; Stability; Multiple time delays; Imaginary spectra

Peng Lin, Wei Ren,
Distributed H∞ constrained consensus problem,
Systems & Control Letters,
Volume 104,
2017,
Pages 45-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2017.02.010.
(http://www.sciencedirect.com/science/article/pii/S0167691117300427)
Abstract: This paper is concerned with the distributed H∞ constrained consensus problem for multi-agent systems. The objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired H∞ performance index in the presence of external disturbances. A nonlinear distributed algorithm is adopted to solve this constrained consensus problem. To measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set, a nonlinear function is constructed as the H∞ output function. By analyzing the convexity of the convex set, a sufficient condition is given to solve the constrained consensus problem with the desired H∞ performance. Finally, a numerical simulation example is provided to show the effectiveness of our theoretical results.
Keywords: Constrained consensus problem; 
               H∞ performance; Multi-agent systems

Vasfi Eldem, Gökhan Şahan,
The effect of coupling conditions on the stability of bimodal systems in R3,
Systems & Control Letters,
Volume 96,
2016,
Pages 141-150,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116301062)
Abstract: This paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in R3. The approach taken allows the vector field to be discontinuous on the switching plane. In this framework, verifiable necessary and sufficient conditions are proposed for global asymptotic stability of bimodal systems being considered. It is further shown that the way the subsystems are coupled on the switching plane plays a crucial role on global asymptotic stability. Along this line, it is demonstrated that a constant (which is called the coupling constant in the paper) can be changed without changing the eigenvalues of subsystems and this change can make bimodal system stable or unstable.
Keywords: Bimodal system; Asymptotic stability; Discontinuous vector field; Piecewise linear systems; Coupling condition

Zupeng Zhou, Yonghong Tan, Peng Shi,
Fault detection of a sandwich system with dead-zone based on robust observer,
Systems & Control Letters,
Volume 96,
2016,
Pages 132-140,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301104)
Abstract: Non-smooth sandwich systems with dead-zone widely exist in the real engineering applications. For accurately detecting its faults, a novel robust observer has been proposed in this paper. With the consideration of the model uncertainties, disturbances, and switching error which specially belongs to the system, the so-called general disturbance is defined. After that, the conventional dynamic robust observer design method can be applied to the system. Then, for saving the computing time and effectively reducing the effect of the disturbances to the residual, the main frequencies of the disturbances have been identified by the spectrum analysis of the residual created by the conventional observer and the zeros assignment methodology has been applied to get one feedback matrix of the robust observer. Finally, the rest of the feedback matrices of the robust observer can be obtained by solving an optimal problem with H∞,F/H−,F as the minimizing object. For verifying the effectiveness of this novel robust observer, the comparison between the proposed robust non-smooth scheme and the conventional method has been made. The final results show that the proposed robust fault detection approach can detect the actuator and sensor faults of the system more accurately and timely with a lower missing and false alarm rates comparing with the conventional one.
Keywords: Robust observer; Dead-zone; Sandwich system; General disturbance; Fault detection

Nikolaos Kariotoglou, Kostas Margellos, John Lygeros,
On the computational complexity and generalization properties of multi-stage and stage-wise coupled scenario programs,
Systems & Control Letters,
Volume 94,
2016,
Pages 63-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116300494)
Abstract: We discuss the computational complexity and feasibility properties of scenario sampling techniques for uncertain optimization programs. We propose an alternative way of dealing with a special class of stage-wise coupled programs and compare it with existing methods in the literature in terms of feasibility and computational complexity. We identify trade-offs between different methods depending on the problem structure and the desired probability of constraint satisfaction. To illustrate our results, an example from the area of approximate dynamic programming is considered.
Keywords: Scenario approach; Randomized optimization; Uncertain systems; Approximate dynamic programming

Philipp Schulze, Benjamin Unger,
Data-driven interpolation of dynamical systems with delay,
Systems & Control Letters,
Volume 97,
2016,
Pages 125-131,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116301347)
Abstract: We present a data-driven realization for systems with delay, which generalizes the Loewner framework. The realization is obtained with low computational cost directly from measured data of the transfer function. The internal delay is estimated by solving a least-square optimization over some sample data. Our approach is validated by several examples, which indicate the need for preserving the delay structure in the reduced model.
Keywords: Data-driven model reduction; Delay systems; Loewner framework; Tangential interpolation; Delay recovery; Structure-preserving model reduction


Editorial Board,
Systems & Control Letters,
Volume 96,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30122-0.
(http://www.sciencedirect.com/science/article/pii/S0167691116301220)

Yutaka Yamamoto,
Behavioral controllability and coprimeness for pseudorational transfer functions,
Systems & Control Letters,
Volume 95,
2016,
Pages 20-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.014.
(http://www.sciencedirect.com/science/article/pii/S0167691115002558)
Abstract: Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bézout identity, image representation, direct sum decomposition, etc., its overall picture for infinite-dimensional systems still remains rather incomplete, in spite of various existing attempts. This article gives an extension of such results in a well-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent. We establish equivalent conditions for controllability in terms of the Bézout identity, relationships with notions such as image representation and direct sum decompositions.
Keywords: Behavioral controllability; Infinite-dimensional behaviors; Pseudorationality; Coprimeness; Bézout identity


Editorial Board,
Systems & Control Letters,
Volume 94,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30089-5.
(http://www.sciencedirect.com/science/article/pii/S0167691116300895)

Lin Tie,
On controllability of discrete-time bilinear systems by near-controllability,
Systems & Control Letters,
Volume 98,
2016,
Pages 14-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.019.
(http://www.sciencedirect.com/science/article/pii/S0167691116301463)
Abstract: In this paper, controllability of discrete-time bilinear systems is studied. By applying a recent result on near-controllability, a new sufficient condition for controllability of the systems is presented, where controllability is proved by approximation with near-controllability. The new condition is algebraically verifiable and is hence easy to apply compared with a classical result on controllability of discrete-time bilinear systems, which can be effective even when the classical result does not work. Furthermore, the control inputs to achieve the transition of the systems between any given pair of states are approximately computable according to near-controllability. Therefore, near-controllability can be used to not only better characterize the system properties, but also prove controllability with computable control inputs. The new condition is then generalized to derive similar results on controllability and near-controllability of the systems. Finally, examples are given to illustrate the results of this paper.
Keywords: Discrete-time bilinear systems; Controllability; Near-controllability; Computable control inputs

Francis D. Lagor, Kayo Ide, Derek A. Paley,
Incorporating prior knowledge in observability-based path planning for ocean sampling,
Systems & Control Letters,
Volume 97,
2016,
Pages 169-175,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116301189)
Abstract: Observability-based path planning of autonomous sampling platforms for flow estimation is a technique by which candidate trajectories are evaluated based on their ability to enhance the observability of underlying flow-field parameters. Until now, observability-based path planning has focused primarily on forward-in-time integration. We present a novel approach that makes use of the background error covariance at the current time to account properly for uncertainty of the underlying flow. The reduced Hessian of an optimal, linear data-assimilation strategy properly accounts for prior knowledge in the linear case and must be full rank to infer the initial state. The reduced Hessian represents an observability Gramian augmented with an inverse prior covariance. We extend this concept to the nonlinear case to yield a new criterion for scoring candidate trajectories: the empirical augmented unobservability index. Solving the differential covariance Riccati equation of the Kalman Filter for deterministic dynamics also properly accounts for prior knowledge in the linear case, but at a later time. The solution to this equation reveals the important distinctions between observability-based, augmented observability-based, and anticipated covariance-based path planning. Path planning based on this unobservability index in the presence of prior information yields the desired behavior in numerical experiments of a guided Lagrangian sensor in a two-vortex flow pertinent to ocean sampling.
Keywords: Observability; Ocean sampling; Path planning

Guanyu Lai, Zhi Liu, C.L. Philip Chen, Yun Zhang,
Adaptive asymptotic tracking control of uncertain nonlinear system with input quantization,
Systems & Control Letters,
Volume 96,
2016,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116300767)
Abstract: Asymptotic tracking control of uncertain nonlinear system with input quantization is an important, yet challenging issue in the field of adaptive control. So far, there is still no result available in addressing this issue even for the case of time-invariant reference signal. In this paper, we solve this problem by proposing a new tuning function control scheme which is designed on the basis of a novel decomposition of hysteresis quantizer. It is proved that the proposed scheme ensures the global boundedness of all closed-loop signals and the asymptotic convergence of tracking error to zero. Moreover, an explicit bound for the L2-norm of the tracking error is derived, which shows that the transient performance can also be improved with the proposed scheme.
Keywords: Adaptive control; Input quantization; Nonlinear systems; Asymptotic tracking

P. Rapisarda, A.C. Antoulas,
Reprint of “A bilinear differential forms approach to parametric structured state-space modelling”,
Systems & Control Letters,
Volume 95,
2016,
Pages 77-82,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.012.
(http://www.sciencedirect.com/science/article/pii/S0167691116300524)
Abstract: We use one-variable Loewner techniques to compute polynomial-parametric models for MIMO systems from vector-exponential data gathered at various points in the parameter space. Instrumental in our approach are the connections between vector-exponential modelling via bilinear differential forms and the Loewner framework.
Keywords: Bilinear differential forms; Loewner approach; Parametric modelling

Haichao Gui, George Vukovich,
Global finite-time attitude tracking via quaternion feedback,
Systems & Control Letters,
Volume 97,
2016,
Pages 176-183,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.017.
(http://www.sciencedirect.com/science/article/pii/S016769111630144X)
Abstract: This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular velocity, and attitude only. In all three scenarios hybrid control techniques are utilized to overcome the well-known topological constraint on the attitude manifold, while coupled nonsmooth feedback inputs are designed via homogeneous theory to achieve finite-time stability. Specially, a finite-time bias observer is derived in the second scenario and a quaternion filter is constructed to provide damping in the absence of velocity feedback. The proposed methods ensure bounded control torques a priori and, in particular, include several existing attitude controllers as special cases.
Keywords: Attitude control; Finite-time stability; Homogeneity; Hybrid control; Output feedback; Saturation

Steffi Knorn, Richard H. Middleton,
Asymptotic and exponential stability of nonlinear two-dimensional continuous–discrete Roesser models,
Systems & Control Letters,
Volume 93,
2016,
Pages 35-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116000621)
Abstract: Sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear two-dimensional continuous–discrete systems are proposed. Special attention is paid to neutrally stable systems such as some two-dimensional system descriptions of vehicle platoons, which may be stable or asymptotically stable but never exponentially stable. Our conditions for Lyapunov stability and asymptotic stability only require the corresponding two-dimensional Lyapunov function to have a negative semidefinite divergence. They are thus suitable for the analysis of non-exponential versions of 2D stability. Examples are given to illustrate the results.
Keywords: Two-dimensional (2D); Nonlinear systems; Stability; Continuous–discrete

Ruth Curtain, Hans Zwart,
Stabilization of collocated systems by nonlinear boundary control,
Systems & Control Letters,
Volume 96,
2016,
Pages 11-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116300809)
Abstract: We design control laws for a class of dissipative infinite-dimensional systems using nonlinear boundary control action. The applications are to saturated control of SCOLE-type models.
Keywords: Semilinear differential equations; Partial differential equations; Dissipative systems; Boundary control

Zhiyong Sun, Shaoshuai Mou, Brian D.O. Anderson, Ming Cao,
Exponential stability for formation control systems with generalized controllers: A unified approach,
Systems & Control Letters,
Volume 93,
2016,
Pages 50-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.022.
(http://www.sciencedirect.com/science/article/pii/S016769111600061X)
Abstract: This paper discusses generalized controllers for distance-based rigid formation shape stabilization and aims to provide a unified approach for the convergence analysis. We consider two types of formation control systems according to different characterizations of target formations: minimally rigid target formation and non-minimally rigid target formation. For the former case, we firstly prove the local exponential stability for rigid formation systems when using a general form of shape controllers with certain properties. From this viewpoint, different formation controllers proposed in previous literature can be included in a unified framework. We then extend the result to the case that the target formation is non-minimally rigid, and show that exponential stability of the formation system is still guaranteed with generalized controllers.
Keywords: Exponential convergence; Graph rigidity; Distance-based formations


Editorial Board,
Systems & Control Letters,
Volume 97,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30159-1.
(http://www.sciencedirect.com/science/article/pii/S0167691116301591)

Lei Ding, Wei Xing Zheng,
Consensus tracking in heterogeneous nonlinear multi-agent networks with asynchronous sampled-data communication,
Systems & Control Letters,
Volume 96,
2016,
Pages 151-157,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116301074)
Abstract: This paper is concerned with the problem of consensus tracking for heterogeneous nonlinear multi-agent systems via asynchronous sampled-data information. Due to the existence of heterogeneity of dynamics and asynchrony of sampled information, the closed-loop error tracking system with ‘disturbance-like’ term can be established. By utilizing the Lyapunov–Krasovskii approach, the bounded consensus condition with the estimate of the tracking error bound is derived. Based on the criterion, an effective method for designing the appropriate consensus controller gain matrices is developed. An illustrative example with the coupled pendulums is given to demonstrate the efficiency of the results obtained in this paper.
Keywords: Heterogeneous multi-agent systems; Consensus tracking; Bounded consensus; Asynchronously sampling

Hanbing Liu, Peng Hu, Ionuţ Munteanu,
Boundary feedback stabilization of Fisher’s equation,
Systems & Control Letters,
Volume 97,
2016,
Pages 55-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116301190)
Abstract: The aim of this work is to design an explicit finite dimensional boundary feedback controller for locally exponentially stabilizing the equilibrium solutions to Fisher’s equation in both L2(0,1) and H1(0,1). The feedback controller is expressed in terms of the eigenfunctions corresponding to unstable eigenvalues of the linearized equation. This stabilizing procedure is applicable for any level of instability, which extends the result of Barbu (2013) for nonlinear parabolic equations. The effectiveness of the approach is illustrated by a numerical simulation.
Keywords: Fisher’s equation; Local stabilization; Boundary feedback controller

Shen Cong,
Stability analysis for planar discrete-time linear switching systems via bounding joint spectral radius,
Systems & Control Letters,
Volume 96,
2016,
Pages 7-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.012.
(http://www.sciencedirect.com/science/article/pii/S0167691116300780)
Abstract: A pair of 2-by-2 matrices can be transformed into the joint forms, which are bound together via an invariant that measures the deformation of their structures with respect to each other. With this, we obtain an approximation of the joint spectral radius of such a pair of matrices from above and then apply it to assessing stability for planar discrete-time linear switching systems.
Keywords: Planar switching systems; Discrete-time; Joint spectral radius; Stability analysis

Bacem Ben Nasser, Khaled Boukerrioua, Michael Defoort, Mohamed Djemai, Mohamed Ali Hammami,
State feedback stabilization of a class of uncertain nonlinear systems on non-uniform time domains,
Systems & Control Letters,
Volume 97,
2016,
Pages 18-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301116)
Abstract: This paper deals with the stabilization problem for a class of uncertain nonlinear systems on non-uniform time domains. Some sufficient conditions are derived to design a state feedback controller for a class of uncertain nonlinear time-varying systems under vanishing perturbations. Using some Gronwall’s integral inequalities, the uniform exponential stability of the closed-loop systems on arbitrary time scales, is guaranteed. Then, based on the Lyapunov theory, new sufficient conditions are proposed to derive the controller which ensures the practical stability of the closed-loop time-invariant nonlinear uncertain system under non-vanishing perturbations. Some examples illustrate these results.
Keywords: Time scales; Stabilization; Nonlinear systems; Exponential stability; Practical stability

Enrique Zuazua,
Stable observation of additive superpositions of Partial Differential Equations,
Systems & Control Letters,
Volume 93,
2016,
Pages 21-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.017.
(http://www.sciencedirect.com/science/article/pii/S0167691116000463)
Abstract: We address the problem of observing the solutions of a given Partial Differential Equation (PDE), submitted to unknown additive perturbations fulfilling another PDE, possibly of different nature. The problem under consideration is motivated by the issue of averaged control and observation. In the latter, one aims at determining the initial datum of a dynamics, submitted to unknown perturbations, by means of measurements done on the average of solutions with respect to the unknown parameters. We do it in two different cases. First, we assume that a given dynamics is perturbed in an additive manner by a state governed by a PDE, but not necessarily of the same type. In particular we consider the additive superposition of multi-physics solutions of wave and heat type, for instance. Assuming the PDEs under consideration have constant coefficients, we prove that, the by now well-known observability properties of PDE (mainly heat and wave equations) from open subsets of the domain where the dynamics evolves, are stable under these additive perturbations. The proof is rather systematic and easy to apply. It consists in composing all but one (the observable one) PDE operators so to reduce the problem to the consideration of a single equation and applying its known observability properties. The same proof leads to very interesting open problems for systems involving PDEs with variable coefficients where commutators lead to non-local lower order perturbations. We then consider a particular case of a PDE depending on a parameter in a continuous manner. We show that the average is governed by the superposition of two distinct solutions, corresponding to the extremal values of the parameter, and experiencing an extra regularizing effect. This allows showing that the averaged observability property holds, for the continuous average, but to the price of losing a finite number of derivatives. This opens a wide range of interesting problems to be explored.
Keywords: Controllability; Parameter dependent Partial Differential Equations; Averages; Additive superposition

H.J. Jongsma, H.L. Trentelman, M.K. Camlibel,
Robust synchronization of coprime factor perturbed networks,
Systems & Control Letters,
Volume 95,
2016,
Pages 62-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.017.
(http://www.sciencedirect.com/science/article/pii/S0167691116000062)
Abstract: This paper deals with robust synchronization of directed and undirected multi-agent networks with uncertain agent dynamics. Given a network with identical nominal dynamics, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. These perturbations are assumed to be stable and have H∞-norm that is bounded by an a priori given desired tolerance. We derive state space equations for dynamic observer based protocols that achieve robust synchronization in the presence of such uncertainty. We obtain an achievable interval, i.e. an interval such that for each value of the tolerance contained in this interval there exists a robustly synchronizing protocol.
Keywords: Synchronization; Linear multi-agent system; Robust control; Algebraic Riccati equation

Xu Chen, Hui Xiao,
Multirate forward-model disturbance observer for feedback regulation beyond Nyquist frequency,
Systems & Control Letters,
Volume 94,
2016,
Pages 181-188,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116300779)
Abstract: A fundamental challenge in digital control arises when the controlled plant is subjected to a fast disturbance dynamics but is only equipped with a relatively slow sensor. Such intrinsic difficulties are, however, commonly encountered in many novel applications such as laser- and electron-beam-based additive manufacturing, human–machine interaction, etc. This paper provides a discrete-time regulation scheme for exact sampled-data rejection of disturbances beyond Nyquist frequency. By introducing a model-based multirate predictor and a forward-model disturbance observer, we show that the inter-sample disturbances can be fully attenuated despite the limitations in sampling and sensing. The proposed control scheme offers several advantages in stability assurance and lucid design intuitions. Verification of the algorithm is conducted on a motion control platform that shares the general characteristics in several advanced manufacturing systems.
Keywords: Digital control; Disturbance beyond Nyquist frequency; Disturbance rejection; Disturbance observer

Shidong Zhai, Qingdu Li,
Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and switching topologies,
Systems & Control Letters,
Volume 94,
2016,
Pages 127-132,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116300019)
Abstract: This paper studies the bipartite synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies. In order to obtain some conditions such that the network achieves bipartite synchronization for any initial conditions, we design a pinning scheme to pin a part of agents. Under the assumptions that all signed graphs are structurally balanced and the nonlinear system satisfies a one-sided Lipschitz condition, we derive conditions under which the network reaches bipartite synchronization for any initial conditions and arbitrary switching signals. For a general switching signal (especially the periodic switching signal), some conditions related to switching signal are obtained. Finally, we present two numerical examples to illustrate the effectiveness of the obtained results.
Keywords: Signed graph; Structural balance; Nonlinear systems; Pinning control

Frédéric Mazenc, Michael Malisoff,
Reduction model approach for linear time-varying systems with input delays based on extensions of Floquet theory,
Systems & Control Letters,
Volume 94,
2016,
Pages 70-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.013.
(http://www.sciencedirect.com/science/article/pii/S0167691116300536)
Abstract: We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We also prove an analogue for discrete time systems, through a discrete time extension of Floquet theory.
Keywords: Delay; Time-varying; Floquet theory; Reduction model

Davor Dragičević,
A version of a theorem of R. Datko for stability in average,
Systems & Control Letters,
Volume 96,
2016,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.015.
(http://www.sciencedirect.com/science/article/pii/S0167691116300810)
Abstract: In this note we obtain a version of the well-known theorem of R. Datko for the notion of the exponential stability in average. We consider both cocycles over flows as well as cocycles over maps.
Keywords: Cocycle; Datko’s theorem; Stability in average

Thomas Lipp, Stephen Boyd,
Antagonistic control,
Systems & Control Letters,
Volume 98,
2016,
Pages 44-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116301505)
Abstract: In antagonistic control we find an input sequence that maximizes (or at least makes large) an objective that is minimized in typical control. Applications include designing inputs to attack a control system, worst-case analysis of a control system, and security assessment of a control system. The antagonistic control problem is not convex, and so cannot be efficiently solved. We present here a powerful convex-optimization-based heuristic for antagonistic control, based on the convex–concave procedure, which can be used to find bad, if not the global worst-case, inputs. We also give an S-procedure-based upper bound for antagonistic control, applicable in cases when the objective and constraints can be described by quadratic inequalities, and use this to verify on examples that our method yields inputs very close to the (global) worst-case.
Keywords: Optimization; Control; Defending against attacks; Convex–concave procedure; S-procedure

J.J. Benjamin Biemond, Wim Michiels,
Estimation of basins of attraction for controlled systems with input saturation and time-delays,
Systems & Control Letters,
Volume 94,
2016,
Pages 84-91,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116300470)
Abstract: Basins of attraction are instrumental to study the effect of input saturation in control systems, as these sets characterise the initial conditions for which the control strategy induces attraction to the desired state. In this paper, we describe these sets when the open-loop system is exponentially unstable and the system is controlled by actuators with both constant time-delays and saturation. Estimates of the basin of attraction are provided and the allowable time-delay in the control loop is determined with a novel piecewise quadratic Lyapunov–Krasovskii functional that exploits the piecewise affine nature of the system. As this approach leads to sufficient, but not to necessary conditions for attractivity, we present simulations for two examples to show the applicability of the results.
Keywords: Time delay; Basins of attraction; Saturation; Lyapunov–Krasovskii functionals

Wei Ren, Junlin Xiong,
Stability and stabilization of switched stochastic systems under asynchronous switching,
Systems & Control Letters,
Volume 97,
2016,
Pages 184-192,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301323)
Abstract: This paper studies the stability and stabilization problems for a class of switched stochastic systems under asynchronous switching. The asynchronous switching refers to that the switching of the candidate controllers does not coincide with the switching of system modes. Two situations are considered: (1) time-delayed switching situation, that is, the switching of the candidate controllers has a lag to the switching of the system modes; (2) mismatched switching situation, the switching of the candidate controllers does not match the switching of the system modes. Using average dwell time and Lyapunov-like function, sufficient conditions are established for stochastic input-to-state stability of the whole system. Also, the stabilizing controller design approach is proposed for switched stochastic linear systems. The minimal average dwell time and the controller gain are achieved. Finally, a numerical example is used to demonstrate the validity of the developed results.
Keywords: Asynchronous switching; Average dwell time; Switched system; Stochastic stability

Debbie Hernández, Fernando Castaños, Leonid Fridman,
Zero-dynamics design and its application to the stabilization of implicit systems,
Systems & Control Letters,
Volume 98,
2016,
Pages 74-78,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116301566)
Abstract: We present a formula that computes the output of an R-controllable, regular, single-input linear time-invariant implicit system in such a way that it has prescribed relative degree and zeros. The formula is inspired on different generalizations of Ackermann’s formula. A possible application is in the context of sliding-mode control of implicit systems where, as the first step, one can use the proposed formula to design a sliding surface with desired dynamic characteristics and, as the second step, apply a higher-order sliding-mode controller to enforce a sliding motion along the resulting sliding surface.
Keywords: Zero placement; Zero dynamics; Implicit systems; Minimum-phase systems

Michael Dorothy, Soon-Jo Chung,
Switched systems with multiple invariant sets,
Systems & Control Letters,
Volume 96,
2016,
Pages 103-109,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116301049)
Abstract: This paper explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of switching limit cycles commonly found in robotic locomotion and flapping flight.
Keywords: Switched systems; Non-equilibrium steady state; Set-based control

Tanmay Rajpurohit, Wassim M. Haddad,
Lyapunov and converse Lyapunov theorems for stochastic semistability,
Systems & Control Letters,
Volume 97,
2016,
Pages 83-90,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116301165)
Abstract: This paper develops Lyapunov and converse Lyapunov theorems for stochastic semistable nonlinear dynamical systems. Semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to (not necessarily isolated) Lyapunov stable in probability equilibrium points determined by the system initial conditions. Specifically, we provide necessary and sufficient Lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous Lyapunov function whose infinitesimal generator decreases along the dynamical system trajectories and is such that the Lyapunov function satisfies inequalities involving the average distance to the set of equilibria.
Keywords: Stochastic semistability; Lyapunov theory; Converse Lyapunov theorems

Atte Aalto,
Output error minimizing back and forth nudging method for initial state recovery,
Systems & Control Letters,
Volume 94,
2016,
Pages 111-117,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116300597)
Abstract: We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs — given that the observer gains are chosen suitably and the system is exactly observable. If the system’s generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator eAteA∗t in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be presented.
Keywords: Back and forth nudging; State estimation; Output error minimization; Observers; Variational data assimilation

É. Gyurkovics, T. Takács,
Multiple integral inequalities and stability analysis of time delay systems,
Systems & Control Letters,
Volume 96,
2016,
Pages 72-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116300871)
Abstract: This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen’s and Wirtinger’s inequalities, as well as the recently presented Bessel–Legendre inequalities of Seuret and Gouaisbaut (2015) and the Wirtinger-based multiple-integral inequalities of Park et al. (2015) and Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.
Keywords: Integral inequalities; Stability analysis; Continuous-time delay systems; Hierarchy of LMIs

Ivan Markovsky,
The most powerful unfalsified model for data with missing values,
Systems & Control Letters,
Volume 95,
2016,
Pages 53-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115002534)
Abstract: The notion of the most powerful unfalsified model plays a key role in system identification. Since its introduction in the mid 80s, many methods have been developed for its numerical computation. All currently existing methods, however, assume that the given data is a complete trajectory of the system. Motivated by the practical issues of data corruption due to failing sensors, transmission lines, or storage devices, we study the problem of computing the most powerful unfalsified model from data with missing values. We do not make assumptions about the nature or pattern of the missing values apart from the basic one that they are a part of a trajectory of a linear time-invariant system. The identification problem with missing data is equivalent to a Hankel structured low-rank matrix completion problem. The method proposed selects rank deficient complete submatrices of the incomplete Hankel matrix. Under specified conditions the kernels of the submatrices form a nonminimal kernel representation of the data generating system. The final step of the algorithm is reduction of the nonminimal kernel representation to a minimal one. Apart from its practical relevance in identification, missing data is a useful concept in systems and control. Classic problems, such as simulation, filtering, and tracking control can be viewed as missing data estimation problems for a given system. The corresponding identification problems with missing data are “data-driven” equivalents of the classical simulation, filtering, and tracking control problems.
Keywords: Most powerful unfalsified model; Exact system identification; Subspace methods; Missing data; Low-rank matrix completion

A. Buscarino, L. Fortuna, M. Frasca,
Forward action to make a system negative imaginary,
Systems & Control Letters,
Volume 94,
2016,
Pages 57-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116300354)
Abstract: In this letter a strategy to make a system negative imaginary is introduced. We prove that a dynamical forward action is effective to do it for Lyapunov stable systems and discuss how to design the forward compensator for SISO and MIMO systems. Some numerical examples are also included.
Keywords: Negative imaginary systems; Forward compensator

A. Donaire, R. Ortega, J.G. Romero,
Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces,
Systems & Control Letters,
Volume 94,
2016,
Pages 118-126,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116300469)
Abstract: To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to Batlle et al. (2009) and Gómez-Estern and van der Schaft (2004), it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by Chang (2014), we propose to consider the inclusion of dissipative forces, going beyond the gyroscopic ones used in standard IDA-PBC. The contribution of our work is the proof that the addition of these two elements provides a non-trivial extension to the basic IDA-PBC methodology. It is also shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.
Keywords: Stability of nonlinear systems; Passivity-based control; Mechanical systems

Masaki Ogura, Victor M. Preciado, Raphaël M. Jungers,
Efficient method for computing lower bounds on the p-radius of switched linear systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 159-164,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116300743)
Abstract: This paper proposes lower bounds on a quantity called Lp-norm joint spectral radius, or in short, p-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear systems and the equilibrium analysis of switched linear economical models, algorithms for computing the p-radius are only available in a very limited number of particular cases. The proposed lower bounds are given as the spectral radius of an average of the given matrices weighted via Kronecker products and do not place any requirements on the set of matrices. We show that the proposed lower bounds theoretically extend and also can practically improve the existing lower bounds. A Markovian extension of the proposed lower bounds is also presented.
Keywords: p-radius; Switched linear systems; Mean stability; Markov processes

Yu Kawano, Ülle Kotta,
Single-experiment observability decomposition of discrete-time analytic systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 193-199,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.016.
(http://www.sciencedirect.com/science/article/pii/S0167691116301438)
Abstract: This paper addresses the single-experiment observability decomposition of discrete-time analytic systems. Unlike the continuous-time case, there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable. In this paper, a necessary and sufficient condition for integrability of observable space is given. As a corollary of this condition it is proven that if the system is reversible, the observability decomposition can be always achieved. Moreover, integrability of observable space is also addressed for delta-domain models of non-uniformly sampled systems.
Keywords: Discrete-time systems; Nonlinear systems; Observable space; Integrability

Carsten W. Scherer,
Lossless H∞-synthesis for 2D systems (special issue JCW),
Systems & Control Letters,
Volume 95,
2016,
Pages 35-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116000402)
Abstract: We study 2D systems with a continuous and discrete time axis. We embed known results about the stability and H∞-performance properties of such systems into multiplier theory from robust control. It is shown that this opens the way for applying recently developed gain-scheduled controller synthesis techniques in order to solve the H∞-design problem for 2D systems without any conservatism. This is presented if the discrete-time axis is either one- or two-sided, the latter leading to non-conservative H∞-synthesis result for infinite string interconnections of identical linear time-invariant systems.
Keywords: 2D systems; H∞-norm; Controller synthesis; Multipliers

Miloje S. Radenkovic, Jae-Do Park,
Almost sure convergence of extremum seeking algorithm using stochastic perturbation,
Systems & Control Letters,
Volume 94,
2016,
Pages 133-141,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116300627)
Abstract: This paper presents an extremum seeking (ES) algorithm where the perturbation signal is a martingale difference sequence (m.d.s.) with a vanishing variance. The measurement noise at the plant output is modeled by a superposition of deterministic component, and a non-stationary colored noise signal. The optimizing set point of the uncertain reference-to-output equilibrium map is estimated by a stochastic approximation (SA)-type algorithm. The algorithm has a vanishing gain sequence dependent on the set point estimates. By utilizing powerful tools of the martingale convergence theory it is proved that with probability one the set point estimates converge to the optimizing equilibrium point, in spite of the presence of a measurement noise. This result is derived without requiring boundedness or any prior condition on the set point estimates.
Keywords: Extremum seeking; Stochastic perturbation; Self-optimizing control; Martingale convergence

Jinlong Lei, Han-Fu Chen, Hai-Tao Fang,
Primal–dual algorithm for distributed constrained optimization,
Systems & Control Letters,
Volume 96,
2016,
Pages 110-117,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116301050)
Abstract: The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraints assigned to the agents. Based on the augmented Lagrange method, a distributed primal–dual algorithm with a projection operation included is proposed to solve the problem. It is shown that with appropriately chosen constant step size, the local estimates derived at all agents asymptotically reach a consensus at an optimal solution. In addition, the value of the cost function at the time-averaged estimate converges with rate O(1k) to the optimal value for the unconstrained problem. By these properties, the proposed primal–dual algorithm is distinguished from the existing algorithms for distributed constrained optimization. The theoretical analysis is justified by numerical simulations.
Keywords: Distributed constrained optimization; Primal–dual algorithm; Augmented Lagrange method; Multi-agent network

Bo Wei, Feng Xiao,
Event-triggered control for synchronization of coupled harmonic oscillators,
Systems & Control Letters,
Volume 97,
2016,
Pages 163-168,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116301335)
Abstract: This paper addresses the synchronization problem of coupled harmonic oscillators by event-triggered control. A centralized event-triggered control strategy is first developed and is further extended to a decentralized counterpart, in which the control protocol and event-triggering conditions only require local information. With the event-triggered control strategies, controllers update at the discrete instants when the related measurement errors exceed some proper state-dependent thresholds, which can reduce the computation and transmission costs. By the tools from nonsmooth analysis, it is shown that the proposed event-triggered control strategies synchronize asymptotically all oscillator states. Furthermore, a decentralized event-triggered strategy with a fixed threshold is proposed for the sake of excluding the Zeno behavior. The effectiveness of the proposed strategies is illustrated by numerical simulations.
Keywords: Synchronization; Coupled harmonic oscillators; Event-triggered control; Sampled-data control

Aneel Tanwani, Christophe Prieur, Mirko Fiacchini,
Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization,
Systems & Control Letters,
Volume 94,
2016,
Pages 46-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116300482)
Abstract: We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.
Keywords: Event-triggered sampling; Dynamic output feedback; Quantized control; Limited information control; Linear deterministic systems

Z. Bartosiewicz, Ü. Kotta, T. Mullari, M. Tõnso, M. Wyrwas,
On accessibility conditions for state space nonlinear control systems on homogeneous time scales,
Systems & Control Letters,
Volume 98,
2016,
Pages 8-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.018.
(http://www.sciencedirect.com/science/article/pii/S0167691116301451)
Abstract: An algebraic formalism for nonlinear control systems defined on homogeneous time scales is introduced. This formalism is based on the forward, backward shifts, delta and nabla operators of differential one-forms and vector fields. The accessibility conditions for considered control systems both in terms of vector fields and one-forms are presented.
Keywords: Nonlinear system; Time scale; Vector field; One-form; Nabla and delta operators; Accessibility

Yusheng Wei, Zongli Lin,
Stabilization of exponentially unstable discrete-time linear systems by truncated predictor feedback,
Systems & Control Letters,
Volume 97,
2016,
Pages 27-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116301177)
Abstract: Predictor state feedback solves the problem of stabilizing a discrete-time linear system with input delay by predicting the future state with the solution of the state equation and thus rendering the closed-loop system free of delay. The solution of the state equation contains a term that is the convolution of the past control input with the state transition matrix. Thus, the implementation of the resulting predictor state feedback law involves iterative calculation of the control signal. A truncated predictor feedback law results when the convolution term in the state prediction is discarded. When the feedback gain is constructed from the solution of a certain parameterized Lyapunov equation, the truncated predictor feedback law has been shown to achieve asymptotic stabilization of a system that is not exponentially unstable in the presence of an arbitrarily large delay by tuning the value of the parameter small enough. In this paper, we extend this result to exponentially unstable systems. Stability analysis leads to a bound on the delay and a range of the values of the parameter for which the closed-loop system is asymptotically stable as long as the delay is within the bound. The corresponding output feedback result is also derived.
Keywords: Discrete-time; Exponentially unstable systems; Stabilization; Time delay; Truncated predictor feedback


Editorial Board,
Systems & Control Letters,
Volume 95,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30064-0.
(http://www.sciencedirect.com/science/article/pii/S0167691116300640)

Dan Goreac, Alexandra Claudia Grosu, Eduard-Paul Rotenstein,
Approximate and approximate null-controllability of a class of piecewise linear Markov switch systems,
Systems & Control Letters,
Volume 96,
2016,
Pages 118-123,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116300998)
Abstract: We propose an explicit, easily-computable algebraic criterion for approximate null-controllability of a class of general piecewise linear switch systems with multiplicative noise. This gives an answer to the general problem left open in Goreac and Martinez (2015). The proof relies on recent results in Confortola et al. (2015) allowing to reduce the dual stochastic backward system to a family of ordinary differential equations. Second, we prove by examples that the notion of approximate controllability is strictly stronger than approximate null-controllability. A sufficient criterion for this stronger notion is also provided. The results are illustrated on a model derived from repressed bacterium operon (given in Krishna et al. (2005) and reduced in Crudu et al. (2009)).
Keywords: Approximate (null-)controllability; Controlled Markov switch process; Invariance; Stochastic gene networks

S. Mou, Z. Lin, L. Wang, D. Fullmer, A.S. Morse,
Reprint of “A distributed algorithm for efficiently solving linear equations and its applications (Special Issue JCW)”,
Systems & Control Letters,
Volume 95,
2016,
Pages 46-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116300512)
Abstract: A distributed algorithm is proposed for solving a linear algebraic equation Ax=b over a multi-agent network, where A∈Rn̄×n and the equation has a unique solution x∗∈Rn. Each agent knows only a subset of the rows of [Ab], controls a state vector xi(t) of size smaller than n and is able to receive information from its nearby neighbors. Neighbor relations are characterized by time-dependent directed graphs. It is shown that for a large class of time-varying networks, the proposed algorithm enables each agent to recursively update its own state by only using its neighbors’ states such that all xi(t) converge exponentially fast to a specific part of x∗ of interest to agent i. Applications of the proposed algorithm include solving the least square solution problem and the network localization problem.
Keywords: Distributed algorithms; Least-square solution; Network localization

Bai-Nan Liu, Driss Boutat, Da-Yan Liu,
Backstepping observer-based output feedback control for a class of coupled parabolic PDEs with different diffusions,
Systems & Control Letters,
Volume 97,
2016,
Pages 61-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301207)
Abstract: This paper aims to design a backstepping observer-based output feedback controller for a class of coupled parabolic Partial Differential Equations (PDEs) with different diffusions. The considered system is endowed with a sensor at the left boundary and an actuation at the right boundary. Firstly, a backstepping observer is designed. Secondly, compared to the existing literature a weaker condition is deduced to guarantee the stability of the plant system by means of a controller. Thirdly, using the separation principle, an observer-based output feedback controller is set up based on the designed observer and controller. Finally, the efficiency of the proposed method is shown by taking a simplified model of Chemical Tubular Reactor.
Keywords: Coupled parabolic partial differential equations; Observer-based output feedback control; Backstepping observer; Backstepping control; Lyapunov function

Chirayu D. Athalye, Debasattam Pal, Harish K. Pillai,
ℓ∞-stability analysis of discrete autonomous systems described by Laurent polynomial matrix operators,
Systems & Control Letters,
Volume 93,
2016,
Pages 13-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116000633)
Abstract: In this paper, we analyze the ℓ∞-stability of infinite dimensional discrete autonomous systems, whose dynamics is governed by a Laurent polynomial matrix A(σ,σ−1) in shift operator σ on vector valued sequences. We give necessary and sufficient conditions for the ℓ∞-stability of such systems. We also give easy to check tests to conclude or to rule out the ℓ∞-stability of such systems.
Keywords: ℓ∞-stability; Infinite dimensional autonomous systems; 2-D autonomous systems

Mengtao Cao, Feng Xiao, Long Wang,
Second-order consensus in time-delayed networks based on periodic edge-event driven control,
Systems & Control Letters,
Volume 96,
2016,
Pages 37-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.001.
(http://www.sciencedirect.com/science/article/pii/S016769111630086X)
Abstract: The second-order consensus problems in multi-agent systems with undirected topologies and time-invariant delays are considered in this paper. The time-delay robustness of a consensus protocol based on periodic edge-event driven control is investigated, and the studied protocol can largely reduce the communication and controller-updating costs. The relationship between time delays and event-detecting period is characterized. By Lyapunov methods, it is shown that the protocol can solve state consensus problems when the interaction topology is connected, and the system does not exhibit Zeno behavior. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.
Keywords: Consensus; Sampled-data control; Edge events; Time delays

Peter Benner, Pawan Goyal,
Multipoint interpolation of Volterra series and H2-model reduction for a family of bilinear descriptor systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 1-11,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116301141)
Abstract: In this paper, we investigate interpolatory model order reduction for large-scale bilinear descriptor systems. Recently, it was shown in Wyatt et al. (2013) for linear descriptor systems that directly extending the standard rational interpolation conditions used in H2 optimal model reduction to descriptor systems, in general, yields an unbounded error in the H2-norm. This is due to the possible mismatch of the polynomial part of the original and reduced-order systems. This conclusion holds for nonlinear systems as well. In this paper, we deal with bilinear descriptor systems and aim to pay attention to the polynomial part of the bilinear descriptor system along with interpolation. To this end, we have shown in Goyal et al. (2015) how to determine the polynomial part of each subsystem of the bilinear descriptor system explicitly, by assuming special structures of the system matrices. Considering the same structured bilinear descriptor systems, in this paper we first show how to achieve multipoint interpolation of the underlying Volterra series of bilinear descriptor systems while retaining the polynomial part of each subsystem of the bilinear system. Then, we extend the interpolation based first-order necessary conditions for H2 optimality to bilinear descriptor systems and propose an iterative scheme to obtain an H2 optimal reduced-order system. By means of various numerical examples, we demonstrate the efficiency of the proposed model order reduction technique and compare it with reduced bilinear systems obtained by using linear IRKA, the Loewner method for bilinear systems and POD-based approximations.
Keywords: Interpolatory model reduction; Bilinear descriptor systems; Volterra series; H2 optimality

L. Rodríguez-Guerrero, V.L. Kharitonov, S. Mondié,
Robust stability of dynamic predictor based control laws for input and state delay systems,
Systems & Control Letters,
Volume 96,
2016,
Pages 95-102,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116301025)
Abstract: The robust stability properties of the dynamic predictor scheme for state and input delay systems are analyzed in the frequency domain. Robust stability bounds are presented for the cases of uncertainty of the matrix parameters, of the state or input delay, and of the combination of both. An example illustrates the results.
Keywords: Linear time delay system; Input and state delay; Robust stability; Dynamic predictor scheme

Harry L. Trentelman, Paolo Rapisarda,
Preface: SI JCW,
Systems & Control Letters,
Volume 95,
2016,
Pages 1-2,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116300573)

Debasish Chatterjee, Masaaki Nagahara, Daniel E. Quevedo, K.S. Mallikarjuna Rao,
Characterization of maximum hands-off control,
Systems & Control Letters,
Volume 94,
2016,
Pages 31-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116300330)
Abstract: Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necessary conditions for a maximum hands-off optimal control problem using an L0-norm, and also provides sufficient conditions for the optimality of such controls. Numerical example illustrates that adopting an L0 cost leads to a sparse control, whereas an L1-relaxation in singular problems leads to a non-sparse solution.
Keywords: Maximum hands-off control; L0 optimal control; Sparse control

Lin Tie,
On controllability, near-controllability, controllable subspaces, and nearly-controllable subspaces of a class of discrete-time multi-input bilinear systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 36-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.007.
(http://www.sciencedirect.com/science/article/pii/S016769111630113X)
Abstract: This paper considers a class of discrete-time multi-input inhomogeneous bilinear systems. The structure of such systems is most close to linear time-invariant systems’ but they own a strong property. That is, if the systems are uncontrollable, they can still be nearly controllable. Necessary and sufficient conditions for controllability and near-controllability of the systems are established by using a classical decomposition. Furthermore, a geometric characterization is given for the systems such that controllable subspaces and nearly-controllable subspaces are derived and characterized. Similar results on controllability are also obtained for the continuous-time counterparts of the systems. Finally, examples are provided to demonstrate the conceptions and results of this paper.
Keywords: Discrete-time bilinear systems; Inhomogeneous systems; Controllability; Near-controllability; Controllable subspaces; Nearly-controllable subspaces

Alexander Domoshnitsky, Emilia Fridman,
A positivity-based approach to delay-dependent stability of systems with large time-varying delays,
Systems & Control Letters,
Volume 97,
2016,
Pages 139-148,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116301384)
Abstract: In this paper we propose new explicit tests for positivity and exponential stability of systems with large time-varying delays. Our approach is based on nonoscillation of solutions of the corresponding diagonal scalar delay differential equations. Numerical examples illustrate the efficiency of the results.
Keywords: Time-delay systems; Exponential stability; Positive systems

Tian Xia, Luca Scardovi,
Output-feedback synchronizability of linear time-invariant systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 152-158,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116300731)
Abstract: The paper studies the output-feedback synchronization problem for a network of identical, linear time-invariant systems. A criterion to test network synchronization is derived and the class of output-feedback synchronizable systems is introduced and characterized by sufficient and necessary conditions. In particular it is observed that output-feedback stabilizability is sufficient but not necessary for output-feedback synchronizability. In the special case of single-input single-output systems, conditions are derived in the frequency domain. The theory is illustrated with several examples.
Keywords: Synchronization; Linear systems; Output-feedback

Fernando Castaños, Dmitry Gromov,
Passivity-based control of implicit port-Hamiltonian systems with holonomic constraints,
Systems & Control Letters,
Volume 94,
2016,
Pages 11-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116300299)
Abstract: Implicit port-Hamiltonian representations of mechanical systems are considered from a control perspective. Energy shaping is used for the purpose of stabilizing a desired equilibrium. When using implicit models, the problem turns out to be a simple quadratic programming problem (as opposed to the partial differential equations that need to be solved when using explicit representations). The described approach is generalized to address the problem of stabilization of homoclinic orbits thus leading to the formulation of swing-up strategies for underactuated systems.
Keywords: Hamiltonian dynamics; Holonomic constraints; Implicit models; Passivity; Pendulum; Swing-up

Vakhtang Lomadze,
Converting high order linear PDEs to first order,
Systems & Control Letters,
Volume 94,
2016,
Pages 107-110,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116300603)
Abstract: A straightforward way requiring no calculations is offered to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs.
Keywords: Polynomial matrix; PDE; Exact sequence

P. Pepe,
Stabilization of retarded systems of neutral type by control Lyapunov–Krasovskii functionals,
Systems & Control Letters,
Volume 94,
2016,
Pages 142-151,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.015.
(http://www.sciencedirect.com/science/article/pii/S016769111630055X)
Abstract: This paper deals with the stabilization and the practical stabilization of nonlinear systems described by neutral functional differential equations in Hale’s form, affine in the control input. Artstein’s methodology and Sontag’s universal formula are investigated for this class of systems, by means of invariantly differentiable control Lyapunov–Krasovskii functionals.
Keywords: Retarded systems of neutral type; Practical stability; Control Lyapunov–Krasovskii functionals; Artstein’s methodology; Sontag’s universal formula; Time delays

Ambrose A. Adegbege, Zachary E. Nelson,
A Gauss–Seidel type solver for the fast computation of input-constrained control systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 132-138,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116301414)
Abstract: An important class of nonlinear control systems can be represented as the feedback interconnection of two parts: a linear time-invariant system and a block of decentralized nonlinearities. When the linear time-invariant part has a nontrivial feedthrough term or the nonlinearity has a feedback gain, control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant. The requirements for such online computation may result in several implementation issues, especially in real-time and embedded control applications. This paper considers the implementation of such algebraic loops arising from several input-constrained systems. The proposed solution algorithm is globally convergent for a very large class of feedthrough or feedback gains and shows promise for real-time and embedded control applications where a fast but approximate solution is of the essence.
Keywords: Multivariable algebraic loop; Gradient methods; Projected Gauss–Seidel; Embedded constrained control

Jonathan N. Dehaye, Joseph J. Winkin,
Parameterization of positively stabilizing feedbacks for single-input positive systems,
Systems & Control Letters,
Volume 98,
2016,
Pages 57-64,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116301657)
Abstract: This paper provides parameterizations of all positively stabilizing feedbacks for a particular class of finite-dimensional single-input positive systems, a method to yield these parameterizations by means of tools of linear programming and a convergence analysis which allows to extend the results to a particular infinite-dimensional system described by a parabolic partial differential equation. It also provides an academic standard example – the pure diffusion equation – to support the theoretical results.
Keywords: Positive systems; Positive stabilization; Feedback parameterization; Finite differences; Partial differential equations; Convergence analysis; Diffusion equation

Nicolas Perrin, Philipp Schlehuber-Caissier,
Fast diffeomorphic matching to learn globally asymptotically stable nonlinear dynamical systems,
Systems & Control Letters,
Volume 96,
2016,
Pages 51-59,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.018.
(http://www.sciencedirect.com/science/article/pii/S0167691116300846)
Abstract: We propose a new diffeomorphic matching algorithm and use it to learn nonlinear dynamical systems with the guarantee that the learned systems have global asymptotic stability. For a given set of demonstration trajectories, and a reference globally asymptotically stable time-invariant system, we compute a diffeomorphism that maps forward orbits of the reference system onto the demonstrations. The same diffeomorphism deforms the whole reference system into one that reproduces the demonstrations, and is still globally asymptotically stable.
Keywords: Nonlinear dynamical systems; Diffeomorphic mapping; Imitation learning; Lyapunov stability; Dynamical movement primitives

Yûki Nishimura,
Conditions for local almost sure asymptotic stability,
Systems & Control Letters,
Volume 94,
2016,
Pages 19-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116300329)
Abstract: In this paper, we investigate local asymptotic stability ensured by the addition of Gaussian white noise into dynamical systems. There are different stability notions for stochastic systems, such as asymptotic stability in probability (ASiP) and uniform almost sure asymptotic stability (UASAS). The local ASiP property is incapable of ensuring that sample paths converge to the origin with probability one, whereas the local UASAS property is capable of it. However, in general, the local UASAS property requires tight conditions. Here, we provide our notion of local almost sure asymptotic stability (local ASAS) to relax the conditions with both almost sure convergence of sample paths to the origin and the existence of bounded (weak) invariant sets. We find that the addition of Gaussian white noise always prevents the origin from being locally UASAS as long as we consider smooth Lyapunov functions; however, it is possible to make the origin locally ASAS. The result is confirmed by a simple example of elimination of unstable equilibria by deliberately adding Gaussian white noise.
Keywords: Stochastic Lyapunov function; Almost sure asymptotic stability; Weak invariant set; Stabilization by noise

Vakhtang Lomadze,
Proper representations of (multivariate) linear differential systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 25-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116300342)
Abstract: A proper representation of a linear differential system is a representation with no singularity at infinity. It is shown that such a representation always exists. It turns out that for proper representations having minimal number of rows is equivalent to having minimal total row degree. One is led therefore to a natural definition of the notion of minimality. What is remarkable is that a minimal proper representation is uniquely determined up to premultiplication by a unimodular polynomial matrix of special form. This uniqueness result allows, in particular, to introduce important integer invariants.
Keywords: LTI differential system; Graded and filtered modules; Regularity at infinity; WPD property; Proper representation

C. De Persis, P. Tesi,
Networked control of nonlinear systems under Denial-of-Service,
Systems & Control Letters,
Volume 96,
2016,
Pages 124-131,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116301037)
Abstract: We investigate the analysis and design of a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time that feedback information can be lost without resulting in instability of the system. Motivated by the presence of a digital channel we consider event-based controllers for which a minimal inter-sampling time is explicitly characterized.
Keywords: Cyber-physical systems; Networked control systems; Nonlinear control systems; Jamming; Stability analysis

Jovan Stefanovski, Dušan Georgijević,
Interpolation with constraint on frequency region and systems & control application,
Systems & Control Letters,
Volume 97,
2016,
Pages 70-82,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116301153)
Abstract: This paper elaborates on a bitangential interpolation problem with a norm constraint of the interpolant on a given frequency region (and on its generalization), and proves that it admits a solution. A motivation from systems & control for the problem is given, and the solution is applied for construction of a stabilizing control for one-block plants such that the closed-loop transfer matrix is norm-constrained on the frequency region. Illustrative numerical examples are given.
Keywords: Interpolation; Frequency region; Poles and zeros of rational matrices; Invariant zeros; Optimal ℋ∞ control

Timo Reis, Matthias Voigt,
Reprint of “The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions”,
Systems & Control Letters,
Volume 95,
2016,
Pages 3-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116300500)
Abstract: The Kalman–Yakubovich–Popov lemma is a central result in systems and control theory which relates the positive semidefiniteness of a Popov function on the imaginary axis to the solvability of a linear matrix inequality. In this paper we prove sufficient conditions for the existence of a nonpositive solution of this inequality for differential-algebraic systems. Our conditions are given in terms of positivity of a modified Popov function in the right complex half-plane. Our results also apply to non-controllable systems. Consequences of our results are bounded real and positive real lemmas for differential-algebraic systems.
Keywords: Differential-algebraic equation; Kalman–Yakubovich–Popov lemma; Popov function; Bounded real lemma; Positive real lemma

Emmanuelle Crépeau,
Exact boundary controllability of the Korteweg–de Vries equation with a piecewise constant main coefficient,
Systems & Control Letters,
Volume 97,
2016,
Pages 157-162,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.012.
(http://www.sciencedirect.com/science/article/pii/S0167691116301396)
Abstract: This article proposes some interface conditions for a Korteweg–de Vries (KdV) equation with a piecewise constant main coefficient. The well-posedness of the Cauchy problem is proved by using multiplier technique and then an observability inequality for the adjoint problem is obtained. We end up this article with a result of local exact controllability of the discontinuous main coefficient KdV equation with a right Neumann boundary control provided that the length of the domain is small enough and the time of control is sufficiently large.
Keywords: Control; Korteweg–de Vries; HUM; Multiplier method

Mauro Bisiacco, Ingrid Blumthaler, Maria Elena Valcher,
The consensus problem in the behavioral approach,
Systems & Control Letters,
Volume 95,
2016,
Pages 11-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.010.
(http://www.sciencedirect.com/science/article/pii/S016769111500211X)
Abstract: In this paper we investigate the multi-agent consensus problem in a broad context, by assuming both for the agents and for the distributed controllers higher order input–output dynamic models. The behavioral approach developed by Jan Willems seems to be the most appropriate set-up where to investigate this general problem. By making use of the behavioral approach, we will show that the consensus problem can be naturally rephrased as a special case of stabilization problem: the stabilization pertains only a part of the system variables (the outputs) and it is achieved through regular full interconnection of the agent models and of the controllers. It turns out that if the communication among agents is described by a weighted, undirected and connected graph, then a necessary and sufficient condition for the consensus problem to be solvable is that the output is stabilizable from the input in the agents model. In this respect, the theory here developed for higher-order input–output models naturally extends the results about consensus derived in the state-space approach.
Keywords: Behavioral approach; Consensus; Multi-agent system

Shiping Yang, Jian-Xin Xu, Xuefang Li,
Iterative learning control with input sharing for multi-agent consensus tracking,
Systems & Control Letters,
Volume 94,
2016,
Pages 97-106,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.017.
(http://www.sciencedirect.com/science/article/pii/S0167691116300585)
Abstract: In this paper, a novel iterative learning control (ILC) scheme with input sharing is presented for multi-agent consensus tracking. In many ILC works for multi-agent coordination problem, each agent maintains its own input learning, and the input signal is corrected by local measurements over iteration domain. If the agents are allowed to share their learned inputs among them, the strategy can improve the learning process as more learning resources are available. In this work, we develop a new type of learning controller by considering the input sharing among agents, which includes the traditional ILC strategy as a special case. The convergence condition is rigorously derived and analyzed as well. Furthermore, the proposed controller is extended to multi-agent systems under iteration-varying graph. It turns out that the developed controller is very robust to communication variations. In the numerical study, three illustrative examples are presented to show the effectiveness of the proposed controller. The learning controller with input sharing demonstrates not only faster convergence but also smooth transient performance.
Keywords: Multi-agent system; Consensus tracking; Input sharing; Iteration-varying graph

Debasattam Pal, Harish K. Pillai,
Multidimensional behaviors: The state-space paradigm,
Systems & Control Letters,
Volume 95,
2016,
Pages 27-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.012.
(http://www.sciencedirect.com/science/article/pii/S0167691116000414)
Abstract: For 1-D systems, the state-space approach has perhaps become the most popular method of analyzing these systems. Central to the idea of the state-space approach is the ability to write the system equations in a first-order form by introducing new variables called the state variables. There have been several attempts to imitate the state-space framework for n-D systems. Introduction of behavioral theory by Jan C. Willems, has given fresh impetus to this attempt to imitate state-space framework for n-D systems. In this paper, dedicated to Jan Willems, we provide our recent attempt at obtaining a state-space framework for n-D systems.
Keywords: Behaviors; n-D systems; State space; Noether normalization


Editorial Board,
Systems & Control Letters,
Volume 98,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30170-0.
(http://www.sciencedirect.com/science/article/pii/S0167691116301700)

Boyi Ni, Qinghua Zhang,
Stability of the Kalman filter for continuous time output error systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 172-180,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.006.
(http://www.sciencedirect.com/science/article/pii/S016769111630072X)
Abstract: The stability of the Kalman filter is usually ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. This paper studies the case of continuous time output error systems, in which the process noise is totally absent. The classical stability analysis assuming the controllability regarding the process noise is thus not applicable. It is shown in this paper that the uniform complete observability alone is sufficient to ensure the asymptotic stability of the Kalman filter applied to time varying output error systems, regardless of the stability of the considered systems themselves. The exponential or polynomial convergence of the Kalman filter is then further analyzed for particular cases of stable or unstable output error systems.
Keywords: Kalman filter; Stability; Output error system

Alessandro Casavola, Emanuele Garone, Francesco Tedesco,
A parallel distributed supervision strategy for multi-agent networked systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 115-124,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.015.
(http://www.sciencedirect.com/science/article/pii/S0167691116301426)
Abstract: This paper introduces a novel parallel distributed supervision strategy for interconnected linear systems subject to pointwise-in-time set-membership coordination constraints. The scheme is based on the Feed Forward Command Governor paradigm. It is assumed that the systems are locally regulated, possibly dynamically coupled, and connected via data links. The supervisor is in charge of enforcing coordination constraints by modifying, whenever necessary, the nominal reference signals so that the global coordination goal is achieved. The proposed method extends in a substantial way the sequential Distributed Command Governor previously developed by the authors by allowing each agent to modify its local reference in parallel with the others. The main idea consists in bounding each subsystem with a set of local artificial constraints able to ensure global constraints satisfaction. These virtual constraints are dynamically generated in a distributed way on the basis of the common information available to all agents. The proposed strategy is described and its properties analyzed. The performance of the obtained scheme is compared with previous solutions in the final example.
Keywords: Control of constrained systems; Reference management; Distributed control

Herbert Mangesius, Jean-Charles Delvenne, Sanjoy K. Mitter,
Gradient and passive circuit structure in a class of non-linear dynamics on a graph,
Systems & Control Letters,
Volume 96,
2016,
Pages 30-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.019.
(http://www.sciencedirect.com/science/article/pii/S0167691116300858)
Abstract: We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the assumption of detailed balance, we provide a method to formulate the governing ODE system in gradient descent form of sum-separable energy functions, which thus represent a class of Lyapunov functions; this class coincides with Csiszár’s information divergences. Our approach bases on a transformation of the original problem to a mass-preserving transport problem and it reflects a little-noticed general structure result for passive network synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed gradient formulation extends known gradient results in dynamical systems obtained recently by M. Erbar and J. Maas in the context of porous medium equations. Furthermore, we exhibit a novel relationship between inhomogeneous Markov chains and passive non-linear circuits through gradient systems, and show that passivity of resistor elements is equivalent to strict convexity of sum-separable stored energy. Eventually, we discuss our results at the intersection of Markov chains and network systems under sinusoidal coupling.
Keywords: Dynamics on a graph; Gradient flows; Passive circuits; Information inequalities; Lyapunov functions

Ran Huang, Jinhui Zhang, Zhongwei Lin,
Optimal control of discrete-time bilinear systems with applications to switched linear stochastic systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 165-171,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116300615)
Abstract: This paper aims at characterizing the most destabilizing switching law for discrete-time switched systems governed by a set of bounded linear operators. The switched system is embedded in a special class of discrete-time bilinear control systems. This allows us to apply the variational approach to the bilinear control system associated with a Mayer-type optimal control problem, and a second-order necessary optimality condition is derived. Optimal equivalence between the bilinear system and the switched system is analyzed, which shows that any optimal control law can be equivalently expressed as a switching law. This specific switching law is most unstable for the switched system, and thus can be used to determine stability under arbitrary switching. Based on the second-order moment of the state, the proposed approach is applied to analyze uniform mean-square stability of discrete-time switched linear stochastic systems. Numerical simulations are presented to verify the usefulness of the theoretic results.
Keywords: Discrete-time; Stability analysis; Optimal control; Bilinear system; Switched linear stochastic system

A.M. Perdon, E. Zattoni, G. Conte,
Model matching with strong stability in switched linear systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 98-107,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.009.
(http://www.sciencedirect.com/science/article/pii/S0167691116301360)
Abstract: This work deals with model matching by output dynamic feedback in switched linear systems. The plant and the model are assumed to be subject to different switching signals. A necessary and sufficient condition for achieving model matching with asymptotic stability of both the closed-loop compensated system and the compensator, for a sufficiently large dwell time, is proven. Such condition is obtained by specializing the structural condition with a suitable redefinition of the robust controlled invariant subspace involved, capable of capturing not only the structural aspect of the problem but also the stability aspects. The effect of the combined action of nonzero initial states and nonzero inputs is dealt with. The solution to a more demanding problem formulation, where the dwell time is assumed to be fixed and given is also discussed.
Keywords: Switched systems; Model matching; Output feedback; Dwell time

D. Efimov, E. Fridman, A. Polyakov, W. Perruquetti, J.-P. Richard,
On design of interval observers with sampled measurement,
Systems & Control Letters,
Volume 96,
2016,
Pages 158-164,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116301086)
Abstract: New design of interval observers for continuous-time systems with discrete-time measurements is proposed. For this purpose new conditions of positivity for linear systems with sampled feedback are obtained. A sampled-data stabilizing control is synthesized based on provided interval estimates. Efficiency of the obtained solution is demonstrated on examples.
Keywords: Interval observer; Sampled measurements; Output control

Alex Olshevsky,
Eigenvalue clustering, control energy, and logarithmic capacity,
Systems & Control Letters,
Volume 96,
2016,
Pages 45-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.013.
(http://www.sciencedirect.com/science/article/pii/S0167691116300792)
Abstract: We prove two bounds showing that if the eigenvalues of a matrix are clustered in a region of the complex plane then the corresponding discrete-time linear system requires significant energy to control. A curious feature of one of our bounds is that the dependence on the region is via its logarithmic capacity, which is a measure of how well a unit of mass may be spread out over the region to minimize a logarithmic potential.
Keywords: Linear systems; Discrete-time; Control energy; Control of large scale systems; Eigenvalue clustering

Xuetao Yang, Quanxin Zhu,
Corrigendum to “Stabilization in probability and mean square of controlled stochastic dynamical system with state delay” [Syst. Control Lett. 68 (2014) 95–100],
Systems & Control Letters,
Volume 93,
2016,
Pages 77-81,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116300032)
Abstract: This note mainly corrects Theorem 3.1 contained in Akaninyene (2014). The author may have omitted quadratic variation term of Eq. (2.1) by mistake when using Itô’s integral formula. Some additional minor corrections are also listed.
Keywords: Delay; Exponential stability; Mean square stability; Stochastic dynamical system; Optimal control

Fotis N. Koumboulis,
Common I/O Triangular Decoupling for multi model descriptor systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 108-114,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.013.
(http://www.sciencedirect.com/science/article/pii/S0167691116301402)
Abstract: The problem of Common Input/Output Triangular Decoupling (TD) for multi model descriptor linear systems is solved, using a static state feedback controller. The necessary and sufficient conditions for the solvability of the problem are established. The set of all state feedback controllers solving the problem under the solvability conditions is derived. For the derivation of the above results, the problem of the inversion of a multiparameter matrix pencil in a triangular matrix form and under linear inequality constraints is solved.
Keywords: Multi model systems; Singular systems; I/O Triangular Decoupling

Boyang Ding, Changming Ding,
Recurrence and LaSalle invariance principle,
Systems & Control Letters,
Volume 93,
2016,
Pages 64-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.011.
(http://www.sciencedirect.com/science/article/pii/S0167691116300159)
Abstract: In this paper, we consider three different notions of recurrence, chain recurrence, strong chain recurrence and generalized recurrence, where the generalized recurrence is introduced by Auslander (1964) and the strong chain recurrence is derived from the idea of a strong chain defined by Easton (1978). We prove that for a quasi-gradient flow in a compact metric space, these three recurrences are equivalent. Finally, we establish an invariance principle, i.e., the ω-limit set of a precompact orbit is contained in the generalized recurrent component of ’zero derivative’ set of a Lyapunov function.
Keywords: Chain recurrence; Generalized recurrence; Lyapunov function; Invariance principle

Dong Shen, Wei Zhang, Jian-Xin Xu,
Iterative Learning Control for discrete nonlinear systems with randomly iteration varying lengths,
Systems & Control Letters,
Volume 96,
2016,
Pages 81-87,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301001)
Abstract: This note proposes ILC for discrete-time affine nonlinear systems with randomly iteration varying lengths. No prior information on the probability distribution of random iteration length is required prior for controller design. The conventional P-type update law is used with a modified tracking error because of randomly iteration varying lengths. A novel technical lemma is proposed for the strict convergence analysis in pointwise sense. An illustrative example verifies the theoretical results.
Keywords: Iterative Learning Control; Discrete nonlinear system; Iteration varying lengths; Pointwise convergence; Initial state conditions

Shinsaku Izumi, Shun-ichi Azuma, Toshiharu Sugie,
Stabilization by controller networks,
Systems & Control Letters,
Volume 94,
2016,
Pages 77-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116300548)
Abstract: This paper addresses a design method of controller networks, i.e., networked controllers which cooperatively determine the control inputs by exchanging the information with their neighbors. The problem considered here is to design the controllers stabilizing the resulting feedback system for an unknown network topology. As a solution to the problem, we propose controllers such that the entire network acts as a state feedback controller through a consensus protocol, and derive gain conditions to stabilize the resulting feedback system. This enables us to obtain a controller network that is robust against uncertainties of the network topology.
Keywords: Networked control systems; Distributed control; Cooperative control; Consensus protocols; Controller networks

Joan-Josep Climent, Victoria Herranz, Carmen Perea,
Parallel concatenated convolutional codes from linear systems theory viewpoint,
Systems & Control Letters,
Volume 96,
2016,
Pages 15-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.016.
(http://www.sciencedirect.com/science/article/pii/S0167691116300822)
Abstract: The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input–state–output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.
Keywords: Convolutional code; Concatenated convolutional code; Free distance; Column distances; Observable pair; Controllable pair; Observable convolutional code; Input–state–output representation; Minimal representation

Zhi-Hua Xiao, Yao-Lin Jiang,
Model order reduction of MIMO bilinear systems by multi-order Arnoldi method,
Systems & Control Letters,
Volume 94,
2016,
Pages 1-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116300305)
Abstract: In this paper, we present a time domain model order reduction method for multi-input multi-output (MIMO) bilinear systems by general orthogonal polynomials. The proposed method is based on a multi-order Arnoldi algorithm applied to construct the projection matrix. The resulting reduced model can match a desired number of expansion coefficient terms of the original system. The approximate error estimate of the reduced model is given. And we also briefly discuss the stability preservation of the reduced model in some cases. Additionally, in combination with Krylov subspace methods, we propose a two-sided projection method to generate reduced models which capture properties of the original system in the time and frequency domain simultaneously. The effectiveness of the proposed methods is demonstrated by two numerical examples.
Keywords: Model order reduction; Bilinear systems; General orthogonal polynomials; Multi-order Arnoldi; Stability

Daniel E. Miller,
The role of convexity in the adaptive control of rapidly time-varying systems,
Systems & Control Letters,
Volume 97,
2016,
Pages 91-97,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116301359)
Abstract: In classical adaptive control the parameters are assumed to be fixed or slowly time-varying. In order to facilitate parameter estimation/tuning it is desirable to have the set of admissible parameters lie in a convex set; if this set is not convex, a common trick is to replace it with its convex hull, but the adaptive control problem is challenging if stabilizability of the set of admissible parameters is lost. However, such a convexity assumption is an artifact of the approach to the problem, rather than an inherent constraint, since most logic-based and supervisory approaches to the problem make no such requirement. On the other hand, here we show that losing stabilizability on the convex hull of the set of admissible parameters plays an important role in the adaptive control of rapidly time-varying systems.
Keywords: Adaptive control; Convexity; Time-varying systems

Giacomo Como, Fabio Fagnani,
From local averaging to emergent global behaviors: The fundamental role of network interconnections,
Systems & Control Letters,
Volume 95,
2016,
Pages 70-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116000323)
Abstract: Distributed averaging is one of the simplest and most widely studied network dynamics. Its applications range from cooperative inference in sensor networks, to robot formation, to opinion dynamics. A number of fundamental results and examples scattered through the literature are gathered here and some original approaches and generalizations are presented, emphasizing the deep interplay between the network interconnection structure and the emergent global behavior.
Keywords: Network dynamics; Interconnections; Emergent behaviors; Distributed averaging; Consensus; Polarization; Electrical networks

Shun-Pin Hsu,
Controllability of the multi-agent system modeled by the threshold graph with one repeated degree,
Systems & Control Letters,
Volume 97,
2016,
Pages 149-156,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.09.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116301372)
Abstract: The controllability issue of multi-agent systems modeled by a special class of graphs is studied. Suppose the modeling graph is simple, connected and driven by only one controller. The author shows that the system is controllable if the graph has exactly two vertices with the same degree and either one of these two vertices is selected to receive the control input. This result is extended to the case of the threshold graph that has only one repeated degree. Specifically, it is shown that if the threshold graph has only one repeated degree and its multiplicity is m, then m−1 is the minimum number of the controllers required to make the system controllable. In addition, the necessary and sufficient condition that characterizes the binary control vectors to ensure the controllability of the system is derived.
Keywords: Controllability; Multi-agent systems; Threshold graph

Zbigniew Bartosiewicz,
Invariance and monotonicity of nonlinear systems on time scales,
Systems & Control Letters,
Volume 93,
2016,
Pages 58-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116300160)
Abstract: Invariance of a subset of the state space with respect to a control system on an arbitrary time scale is studied. This includes in particular continuous-time and discrete-time systems. The invariance is characterized with the aid of natural operators associated to the system: shifts and skew derivations. For different time scales the criteria take different forms. Then for polynomial systems algebraic criteria of invariance based on Positivstellensatz from real algebraic geometry are developed. A relation between invariance and monotonicity is exhibited and the results on invariance are used to characterize monotonicity.
Keywords: Invariance; Monotone system; Time scale; Positivstellensatz; Skew derivation

Lijun Zhu, Zhiyong Chen, Richard Middleton,
Robust asymptotic model matching and its application to output synchronization of heterogeneous multi-agent systems,
Systems & Control Letters,
Volume 94,
2016,
Pages 37-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116300287)
Abstract: Output synchronization of heterogeneous multi-agent systems has been one of the most interesting cooperative control problems. This paper first gives a brief survey of the research on the problem from which we see that the problem can be solved in a two-step manner with the aid of a properly designed local reference for each agent: (i) a controller is designed for each agent to achieve the trajectory regulation of the agent output to its associated reference; (ii) network collaboration is added to achieve consensus among references. In the presence of system uncertainties, the robust trajectory regulation problem in (i) can be solved by an internal model design. In this paper, we formulate a novel robust asymptotic model matching problem which is less conservative than trajectory regulation and can be solved by a static controller not relying on an internal model. Moreover, network collaboration is designed in (ii) within the so-called output communication setting such that consensus among references occurs concurrently with robust asymptotic model matching. As a result, output synchronization of heterogeneous multi-agent systems is achieved with a novel approach.
Keywords: Multi-agent systems; Cooperative control; Heterogeneous systems; Robust control; Output regulation

K.V. Sklyar, S.Yu. Ignatovich,
Linearizability of systems of the class C1 with multi-dimensional control,
Systems & Control Letters,
Volume 94,
2016,
Pages 92-96,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.05.016.
(http://www.sciencedirect.com/science/article/pii/S0167691116300561)
Abstract: We give a complete description of nonlinear control systems of the class C1 with multi-dimensional control that are feedback linearizable by means of change of variables of the class C2 and change of controls of the class C1.
Keywords: Systems with multi-dimensional control; Feedback linearizability problem; C1-smooth nonlinear control systems; Lie brackets technique

Tjorben Groß, Stephan Trenn, Andreas Wirsen,
Solvability and stability of a power system DAE model,
Systems & Control Letters,
Volume 97,
2016,
Pages 12-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116301098)
Abstract: The dynamic model of a power system is the combination of the power flow equations and the dynamic description of the generators (the swing equations) resulting in a differential–algebraic equation (DAE). For general DAEs solvability is not guaranteed in general, in the linear case the coefficient matrices have to satisfy a certain regularity condition. We derive a solvability characterization for the linearized power system DAE solely in terms of the network topology. As an extension to previous result we allow for higher order generator dynamics. Furthermore, we show that any solvable power system DAE is automatically of index one, which means that it is also numerically well posed. Finally, we show that any solvable power system DAE is stable but not asymptotically stable.
Keywords: Power systems; DAE; Solvability; Stability

Hongwei Zhang, Yuegang Tao, Zilong Zhang,
Strong solvability of interval max-plus systems and applications to optimal control,
Systems & Control Letters,
Volume 96,
2016,
Pages 88-94,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.07.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116301013)
Abstract: This paper considers the strong solvability of interval max-plus systems. The solvable entry and solvable interval are introduced to establish the necessary and sufficient condition for strong solvability of interval max-plus systems. It is proved that such a criterion is equivalent to the criterion proposed by Cechlárová and Cuninghame-Green. The interval strong solution of interval max-plus systems is described and the necessary and sufficient condition for uniquely strong solvability is given. The method of testing strong solvability of interval max-plus systems is constructive and leads to an effective algorithm. To illustrate our results, a workshop optimal control problem is addressed.
Keywords: Interval max-plus systems; Strong solvability; Uniquely strong solvability; Algorithm; Optimal control

Qian Feng, Sing Kiong Nguang,
Stabilization of uncertain linear distributed delay systems with dissipativity constraints,
Systems & Control Letters,
Volume 96,
2016,
Pages 60-71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.06.017.
(http://www.sciencedirect.com/science/article/pii/S0167691116300834)
Abstract: This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov–Krasovskii functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.
Keywords: Uncertain distributed delay systems; Integral inequality; Dissipativity systems; Robust controllers synthesis

Filippo Cacace, Valerio Cusimano, Alfredo Germani, Pasquale Palumbo,
A state predictor for continuous-time stochastic systems,
Systems & Control Letters,
Volume 98,
2016,
Pages 37-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116301529)
Abstract: This work investigates the state prediction problem for nonlinear stochastic differential systems, affected by multiplicative state noise. This problem is relevant in many state-estimation frameworks such as filtering of continuous-discrete systems (i.e. stochastic differential systems with discrete measurements) and time-delay systems. A very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise-free system. Unfortunately these methods provide the exact solution only for linear systems. Instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant, obtained according to the Carleman embedding technique. The truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation. Simulations support the effectiveness of the proposed state-prediction algorithm in comparison to the aforementioned heuristic method.
Keywords: Nonlinear filtering; Stochastic systems; Nonlinear systems; Kalman filtering; Carleman approximation

W.C. Raffa, L.F.C. Alberto,
A uniform invariance principle for periodic systems with applications to synchronization,
Systems & Control Letters,
Volume 97,
2016,
Pages 48-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.08.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116301128)
Abstract: In this paper, we propose an extension of the invariance principle, which is uniform with respect to parameter uncertainties, for the class of periodic ordinary differential equations. This extension allows the derivative of the auxiliary function V, commonly called a Lyapunov function, to be positive in some bounded sets. This important feature has the potential to simplify the problem of exhibiting a function of Lyapunov-type and allows the application of the principle in systems that cannot be treated with the conventional principle, either due to the nonexistence of a Lyapunov-type function or due to the difficulty in exhibiting it. The extension of the invariance principle is useful to obtain estimates of attractors and regions of attraction that are uniform with respect to parameters. The study of synchronization of periodic coupled systems illustrates an application of the principle.
Keywords: Dynamic systems; Differential equations; Invariance principle; Periodic systems; Synchronization

Pavel Pakshin, Julia Emelianova, Mikhail Emelianov, Krzysztof Gałkowski, Eric Rogers,
Dissipativity and stabilization of nonlinear repetitive processes,
Systems & Control Letters,
Volume 91,
2016,
Pages 14-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116000190)
Abstract: Repetitive processes are characterized by repeated executions of a task defined over a finite duration with resetting after each execution is complete. Also the output from any execution directly influences the output produced on the next execution. The repetitive process model structure arises in the modeling of physical processes and can also be used to effect in the control of other systems, the design of iterative learning control laws where experimental verification of designs has been reported. The existing systems theory for them is, in the main, linear model based. This paper considers nonlinear repetitive processes using a dissipative setting and develops a stabilizing control law with the required conditions expressed in terms of vector storage functions. This design is then extended to stabilization plus disturbance attenuation.
Keywords: Nonlinear repetitive processes; Stability; Dissipativity; Passivity; H∞ disturbance attenuation

Huiping Li, Weisheng Yan, Yang Shi, Yintao Wang,
Periodic event-triggering in distributed receding horizon control of nonlinear systems,
Systems & Control Letters,
Volume 86,
2015,
Pages 16-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115001905)
Abstract: How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.
Keywords: Distributed receding horizon control (DRHC); Event-triggered control; Nonlinear systems; Large-scale systems

Augusto Ferrante, Lorenzo Ntogramatzidis,
Continuous-time singular linear–quadratic control: Necessary and sufficient conditions for the existence of regular solutions,
Systems & Control Letters,
Volume 93,
2016,
Pages 30-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.018.
(http://www.sciencedirect.com/science/article/pii/S0167691116000475)
Abstract: The purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear–quadratic (LQ) optimal control. Indeed, in spite of the vast literature on LQ problems, only recently a sufficient condition for the existence of a non-impulsive optimal control has for the first time connected this equation with the singular LQ optimal control problem. In this paper, we establish four equivalent conditions providing a complete picture that connects the singular LQ problem with the constrained generalized continuous algebraic Riccati equation and with the geometric properties of the underlying system.
Keywords: Riccati equations; Singular LQ problem; Regular solutions

Nicholas Moehle, Stephen Boyd,
A perspective-based convex relaxation for switched-affine optimal control,
Systems & Control Letters,
Volume 86,
2015,
Pages 34-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115001747)
Abstract: We consider the switched-affine optimal control problem, i.e., the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system state. We develop a new reduction of this problem to a mixed-integer convex program (MICP), based on perspective functions. Relaxing the integer constraints of this MICP results in a convex optimization problem, whose optimal value is a lower bound on the original problem value. We show that this bound is at least as tight as similar bounds obtained from two other well-known MICP reductions (via conversion to a mixed logical dynamical system, and by generalized disjunctive programming), and our numerical study indicates it is often substantially tighter. Using simple integer-rounding techniques, we can also use our formulation to obtain an upper bound (and corresponding sequence of control inputs). In our numerical study, this bound was typically within a few percent of the optimal value, making it attractive as a stand-alone heuristic, or as a subroutine in a global algorithm such as branch and bound. We conclude with some extensions of our formulation to problems with switching costs and piecewise affine dynamics.
Keywords: Switched-affine systems; Optimal control; Mixed-integer convex programming; Hybrid systems; Disjunctive programming

Francisco Javier Bejarano, Gang Zheng,
Observability of singular time-delay systems with unknown inputs,
Systems & Control Letters,
Volume 89,
2016,
Pages 55-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.002.
(http://www.sciencedirect.com/science/article/pii/S016769111500242X)
Abstract: In this manuscript we give sufficient conditions guaranteeing the observability of singular linear systems with commensurable delays affected by unknown inputs appearing in both the state equation and the output equation. These conditions allow for the reconstruction of the entire state vector using past and actual values of the system output. The obtained conditions coincide with known necessary and sufficient conditions of singular linear systems without delays.
Keywords: Commensurate delay systems; Observability analysis; Singular systems; Polynomial ring


Editorial Board,
Systems & Control Letters,
Volume 93,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30037-8.
(http://www.sciencedirect.com/science/article/pii/S0167691116300378)

Sergey Vichik, Murat Arcak, Francesco Borrelli,
Stability of an analog optimization circuit for quadratic programming,
Systems & Control Letters,
Volume 88,
2016,
Pages 68-74,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115002315)
Abstract: We study the stability of an analog optimization circuit that solves quadratic programming (QP) problems. The circuit dynamics are modeled as a switched affine system. A piece-wise quadratic Lyapunov function and the KYP lemma are used to derive the stability criterion. The stability criterion characterizes the range of critical circuit parameters for which the QP circuit is globally exponentially stable.
Keywords: Optimization; MPC; Quadratic programming; Analog computation; KYP; Lyapunov function; Hybrid systems

Chuan-Ke Zhang, Yong He, L. Jiang, Min Wu, Hong-Bing Zeng,
Stability analysis of systems with time-varying delay via relaxed integral inequalities,
Systems & Control Letters,
Volume 92,
2016,
Pages 52-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116000591)
Abstract: This paper investigates the stability of linear systems with a time-varying delay. The key problem concerned is how to effectively estimate single integral term with time-varying delay information appearing in the derivative of Lyapunov–Krasovskii functional. Two novel integral inequalities are developed in this paper for this estimation task. Compared with the frequently used inequalities based on the combination of Wirtinger-based inequality (or Auxiliary function-based inequality) and reciprocally convex lemma, the proposed ones can provide smaller bounding gap without requiring any extra slack matrix. Four stability criteria are established by applying those inequalities. Based on three numerical examples, the advantages of the proposed inequalities are illustrated through the comparison of maximal admissible delay bounds provided by different criteria.
Keywords: Time-delay system; Time-varying delay; Stability; Relaxed integral inequality; Linear matrix inequality

Romeo Ortega, Alexey Bobtsov, Anton Pyrkin, Stanislav Aranovskiy,
A parameter estimation approach to state observation of nonlinear systems,
Systems & Control Letters,
Volume 85,
2015,
Pages 84-94,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115001863)
Abstract: A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial conditions. The class of systems for which the method is applicable is identified via two assumptions related to the transformability of the system into a suitable cascaded form and our ability to estimate the unknown parameters. The first condition involves the solvability of a partial differential equation while the second one requires some persistency of excitation-like conditions. The proposed observer is shown to be applicable to position estimation of a class of electromechanical systems, for the reconstruction of the state of power converters and for speed observation of a class of mechanical systems.
Keywords: Parameter estimation; Adaptive observer; Nonlinear systems

Ying Tang, Christophe Prieur, Antoine Girard,
Singular perturbation approximation by means of a H2 Lyapunov function for linear hyperbolic systems,
Systems & Control Letters,
Volume 88,
2016,
Pages 24-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.015.
(http://www.sciencedirect.com/science/article/pii/S0167691115002169)
Abstract: A linear hyperbolic system of two conservation laws with two time scales is considered in this paper. The fast time scale is modeled by a small perturbation parameter. By formally setting the perturbation parameter to zero, the full system is decomposed into two subsystems, the reduced subsystem (representing the slow dynamics) and the boundary-layer subsystem (standing for the fast dynamics). The solution of the full system can be approximated by the solution of the reduced subsystem. This result is obtained by using a H2 Lyapunov function. The estimate of the errors is the order of the perturbation parameter for all initial conditions belonging to H2 and satisfying suitable compatibility conditions. Moreover, for a particular subset of initial conditions, more precise estimates are obtained. The main result is illustrated by means of numerical simulations.
Keywords: Distributed parameter systems; Singular perturbation; Lyapunov methods


Editorial Board,
Systems & Control Letters,
Volume 90,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)00050-5.
(http://www.sciencedirect.com/science/article/pii/S0167691116000505)

F. Cacace, F. Conte, A. Germani, G. Palombo,
Optimal control of linear systems with large and variable input delays,
Systems & Control Letters,
Volume 89,
2016,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115002443)
Abstract: This paper proposes an optimal control law for linear systems affected by input delays. Specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a DDE without distributed terms. The solution can be seen as a chain of predictors whose size depends on the maximum delay.
Keywords: Optimal control; Input delay; Linear time-delay systems

E. Bakolas,
Distributed partitioning algorithms for multi-agent networks with quadratic proximity metrics and sensing constraints,
Systems & Control Letters,
Volume 91,
2016,
Pages 36-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691116000347)
Abstract: We consider a class of Voronoi-like partitioning problems, in which a multi-agent network seeks to subdivide a subset of an affine space into a finite number of cells in the presence of sensing constraints. The cell of this subdivision that is assigned to a particular agent consists exclusively of points that can be sensed by this agent and are closer to it than to any other agent that can also sense them. The proximity between an agent and an arbitrary point is measured in terms of a non-homogeneous quadratic (generalized) distance function, which does not, in general, enjoy the triangle inequality and the symmetry property. One of the consequences of this fact is that the structure of the sublevel sets of the utilized proximity metric does not conform with that of the sensing region of an agent. Due to this mismatch, it is possible that a point may be assigned to an agent which is different from its “nearest” agent simply because the nearest agent cannot sense this point, unless special care is taken. We propose a distributed partitioning algorithm that enables each agent to compute its own cell independently from the other agents when the only information available to it is the positions and the velocities of the agents that lie inside its sensing region. The algorithm is based on an iterative process that adjusts the size of the sensing region of each agent until the associated cell of the latter corresponds to the intersection of its sensing region with the cell that would have been assigned to it in the absence of sensing constraints. The correctness of the proposed distributed algorithm, which successfully handles the aforementioned issues, is studied in detail.
Keywords: Voronoi diagrams; Distributed partitioning algorithms; Sensing constraints

Yuanlong Li, Zongli Lin,
A switching anti-windup design based on partitioning of the input space,
Systems & Control Letters,
Volume 88,
2016,
Pages 39-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115002285)
Abstract: This paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti-windup compensator. The closed-loop system consisting of the plant, the controller and the anti-windup compensator is first equivalently formulated as a linear system with input deadzone. We then partition the input space into several regions. In one of these regions, all inputs saturate with the time-derivative of the saturated input being zero. In each of the remaining regions, there is a unique input that does not saturate. The time derivative of the deadzone function associated with the unsaturating input is zero. By utilizing these special properties of the inputs on an existing piecewise Lyapunov function of the augmented state vector containing the deadzone function of inputs, we design a separate anti-windup gain for each region of the input space. The switching from one anti-windup gain to another is activated when the input signals leave one region for another, which can be implemented online since only the measurement of the input signals is required. Simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches.
Keywords: Actuator saturation; Anti-windup design; Domain of attraction; Input saturation; Piecewise quadratic Lyapunov functions; Switching

Yu Kawano, Toshiyuki Ohtsuka,
Stability criteria with nonlinear eigenvalues for diagonalizable nonlinear systems,
Systems & Control Letters,
Volume 86,
2015,
Pages 41-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115001917)
Abstract: Stability of the linear system, especially the diagonalizable system, can be verified by computing the signs of the real parts of its eigenvalues. In this paper, we generalize this result to the diagonalizable nonlinear system in terms of nonlinear eigenvalues. According to the main results, the unique equilibrium point of the diagonalizable system is globally asymptotically stable if a specific set of nonlinear eigenvalues is not positive at each point in the state space.
Keywords: Nonlinear systems; Nonlinear eigenvalues; Diagonal form; Stability

H. Zwart, Y. Le Gorrec, B. Maschke,
Building systems from simple hyperbolic ones,
Systems & Control Letters,
Volume 91,
2016,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116000220)
Abstract: In this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation (p.d.e.) the existence and uniqueness of solutions to hyperbolic and parabolic p.d.e.’s. Among others, we show that starting with an impedance passive system associated to the undamped wave equation, we can obtain an impedance passive system associated to the heat conduction equation.
Keywords: Infinite-dimensional systems theory; Partial differential equation; Impedance passive

Rafael Serrano,
On the LP formulation in measure spaces of optimal control problems for jump-diffusions,
Systems & Control Letters,
Volume 85,
2015,
Pages 33-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115001759)
Abstract: In this short note we formulate a infinite-horizon stochastic optimal control problem for jump-diffusions of Ito–Levy type as a LP problem in a measure space, and prove that the optimal value functions of both problems coincide. The main tools are the dual formulation of the LP primal problem, which is strongly connected to the notion of sub-solution of the partial integro-differential equation of Hamilton–Jacobi–Bellman type associated with the optimal control problem, and the Krylov regularization method for viscosity solutions.
Keywords: Stochastic control; Jump-diffusion; Linear programming; Occupation measure; Dual formulation; Viscosity solution

V.A. Zaitsev,
Global asymptotic stabilization of periodic nonlinear systems with stable free dynamics,
Systems & Control Letters,
Volume 91,
2016,
Pages 7-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116000189)
Abstract: We consider a nonlinear control system with periodic coefficients. We study the problem of asymptotic stabilization of the equilibrium x=0 of the closed-loop system by state feedback. We assume that the free dynamic system possesses a periodic Lyapunov function ensuring Lyapunov stability of the equilibrium x=0. We have developed a method for constructing a damping control for affine systems with periodic coefficients based on a generalization of weak Jurdjevic–Quinn conditions, using an extension of the notion of the commutator to non-stationary vector fields. Using this approach, we obtain sufficient conditions for uniform local and global asymptotic stabilization of general nonlinear systems, in particular, affine control systems, with periodic coefficients. Stabilization results generalize known results for time-invariant systems to time-varying periodic systems.
Keywords: Periodic nonlinear systems; Uniform global asymptotic stabilization; Affine systems; Bounded state feedback

Anton Selivanov, Alexander Fradkov, Daniel Liberzon,
Adaptive control of passifiable linear systems with quantized measurements and bounded disturbances,
Systems & Control Letters,
Volume 88,
2016,
Pages 62-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115002327)
Abstract: We consider a linear uncertain system with an unknown bounded disturbance under a passification-based adaptive controller with quantized measurements. First, we derive conditions ensuring ultimate boundedness of the system. Then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set. The size of the limit set is defined by the disturbance bound. Finally, we demonstrate applicability of the proposed controller to polytopic-type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle.
Keywords: Adaptive control; Quantization; Disturbance; Passification method

Weimin Chen, Shengyuan Xu, Yun Zou,
Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control,
Systems & Control Letters,
Volume 88,
2016,
Pages 1-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115000821)
Abstract: This paper is concerned with the problem of exponential mean-square stabilization of hybrid neutral stochastic differential delay equations with Markovian switching by delay feedback control. A delay feedback controller is designed in the drift part so that the controlled system is mean-square exponentially stable. We discussed two types of structure controls; that is, state feedback and output injection. The stabilization criteria are derived in terms of linear matrix inequalities.
Keywords: Markovian switching; Neutral stochastic differential delay equation; Delay feedback control; Stabilization

Pierre-Olivier Lamare, Nikolaos Bekiaris-Liberis,
Control of 2×2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking,
Systems & Control Letters,
Volume 86,
2015,
Pages 24-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115001875)
Abstract: We consider the problems of trajectory generation and tracking for general 2×2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output. We solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2×2 linear hyperbolic systems. We apply our approach to a wave PDE with indefinite in-domain and boundary damping. For tracking the desired trajectory we employ a PI control law on the tracking error of the output. We prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel “non-diagonal” Lyapunov functional. We demonstrate that the proposed PI control law compensates in the output the effect of in-domain and boundary disturbances. We illustrate our results with numerical examples.
Keywords: Distributed parameter systems; Hyperbolic systems; Backstepping; Lyapunov function

Gabriele Oliva, Roberto Setola, Christoforos N. Hadjicostis,
Distributed finite-time calculation of node eccentricities, graph radius and graph diameter,
Systems & Control Letters,
Volume 92,
2016,
Pages 20-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.015.
(http://www.sciencedirect.com/science/article/pii/S016769111600044X)
Abstract: The distributed calculation of node eccentricities, graph radius and graph diameter are fundamental steps to tune network protocols (e.g., setting an adequate time-to-live of packets), to select cluster heads, or to execute distributed algorithms, which typically depend on these parameters. Most existing methods deal with undirected topologies and have high memory and/or bandwidth requirements (or simply provide a bound on the diameter to reduce such costs). Other approaches, instead, require nodes able to communicate with their neighbors on a point-to-point basis, thus requiring each node to be aware of its neighbors. In this paper, we consider strongly connected directed graphs or connected undirected graphs, and we develop an algorithm that takes advantage of the robustness and versatility of the max-consensus algorithm, and has low computational, memory and bandwidth requirements. Moreover, the agents communicate by broadcasting messages to their (out-) neighbors without requiring any knowledge on them or needing point-to-point communication capability. Specifically, each node has memory occupation proportional to the number of its neighbors, while the bandwidth for each link at each time instant is O(logn) bits, where n is the number of nodes. The completion time of the proposed algorithm is O(δn) for undirected graphs and O(n2) for directed graphs, where δ is the network diameter.
Keywords: Distributed algorithms; Diameter; Eccentricity; Radius; Max-consensus

Dabo Xu, Xinghu Wang, Zhiyong Chen,
Output regulation of nonlinear output feedback systems with exponential parameter convergence,
Systems & Control Letters,
Volume 88,
2016,
Pages 81-90,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115002455)
Abstract: This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.
Keywords: Nonlinear systems; Output regulation; Internal model; Parameter convergence

Martin Gugat, Emmanuel Trélat, Enrique Zuazua,
Optimal Neumann control for the 1D wave equation: Finite horizon, infinite horizon, boundary tracking terms and the turnpike property,
Systems & Control Letters,
Volume 90,
2016,
Pages 61-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116000219)
Abstract: We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T, by minimizing an objective functional that is the convex sum of the L2-norm of the control and of a boundary Neumann tracking term. We provide an explicit solution of this optimal control problem, showing that if the weight of the tracking term is positive, then the optimal control action is concentrated at the beginning and at the end of the time interval, and in-between it decays exponentially. We show that the optimal control can actually be written in that case as the sum of an exponentially decaying term and of an exponentially increasing term. This implies that, if the time T is large, then the optimal trajectory approximately consists of three arcs, where the first and the third short-time arcs are transient arcs, and in the middle arc the optimal control and the corresponding state are exponentially close to 0. This is an example of a turnpike phenomenon for a problem of optimal boundary control. If T=+∞ (infinite time horizon problem), then only the exponentially decaying component of the control remains, and the norms of the optimal control action and of the optimal state decay exponentially in time. In contrast to this situation, if the weight of the tracking term is zero and only the control cost is minimized, then the optimal control is distributed uniformly along the whole interval [0,T] and coincides with the control given by the Hilbert Uniqueness Method. In addition, we establish a similarity theorem stating that, for every T>0, there exists an appropriate weight λ<1 for which the optimal solutions of the corresponding finite horizon optimal control problem and of the infinite horizon optimal control problem coincide along the first part of the time interval [0,2]. We also discuss the turnpike phenomenon from the perspective of a general framework with a strongly continuous semi-group.
Keywords: Vibrating string; Neumann boundary control; Turnpike phenomenon; Exponential stability; Energy decay; Exact control; Infinite horizon optimal control; Similarity theorem; Receding horizon

Yongfang Liu, Zhiyong Geng,
Finite-time formation control for linear multi-agent systems: A motion planning approach,
Systems & Control Letters,
Volume 85,
2015,
Pages 54-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115001760)
Abstract: This paper investigates the problem of finite-time formation control for multi-agent systems with general linear dynamics. First of all, the considered formation problem is converted into the motion planning problem, where the systems are steered from initial positions to the desired terminal configurations. Then, by using Pontryagin maximum principle, an optimal formation control law is developed for multi-agent systems based on some invertible conditions. With the designed control law, the multi-agent systems can achieve the desired formation in finite time, where the formation configurations and the settling time can be specified in advance according to task requirements. Meanwhile, a performance index is guaranteed to be optimal. Further, it is proved that the formation problem concerned is solved if and only if the linear systems are controllable. Finally, a possible application of the proposed control law to spacecraft formation flying with circular and near-circular reference orbit is illustrated.
Keywords: Finite-time formation; Linear system; Motion planning; Multi-agent system

Daizhan Cheng, Hongsheng Qi, Ting Liu, Yuanhua Wang,
A note on observability of Boolean control networks,
Systems & Control Letters,
Volume 87,
2016,
Pages 76-82,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115002297)
Abstract: The observability of Boolean control networks is investigated. The pairs of states are classified into three classes: (i) diagonal, (ii) h-distinguishable, and (iii) h-indistinguishable. For h-indistinguishable pairs, we construct a matrix W called the transferable matrix, which indicates the control-transferability among h-indistinguishable pairs. Modifying W yields a Boolean matrix U0, which is used as the initial matrix for an iterative algorithm. After finite iterations a stable U∗ is reached, which is called the observability matrix. It is proved that a Boolean control network is observable, if and only if, the last column of U∗, Colr+1(U∗)=1r. Some numerical examples are presented.
Keywords: Boolean control network; Observability matrix; Row degree; Distinguishable index; Semi-tensor product

Mohamed K. Helwa, Zhiyun Lin, Mireille E. Broucke,
On the necessity of the invariance conditions for reach control on polytopes,
Systems & Control Letters,
Volume 90,
2016,
Pages 16-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.016.
(http://www.sciencedirect.com/science/article/pii/S0167691115002571)
Abstract: We study the Reach Control Problem (RCP) to make the solutions of an affine system defined on a polytopic state space reach and exit a prescribed facet of the polytope in finite time without first leaving the polytope. So-called invariance conditions are used to prevent solutions from leaving the polytope through facets which are not designated as the exit facet. These conditions are known to be necessary for solvability of the RCP on polytopes by continuous state feedback. We study whether the invariance conditions are also necessary for solvability of the RCP on polytopes by open-loop controls. We show by way of a counterexample that surprisingly the answer is negative. We identify a suitable class of polytopes for which the invariance conditions remain necessary conditions.
Keywords: Hybrid systems; Piecewise affine feedback; Reach control problem

Viorel Barbu, Gabriela Marinoschi,
An optimal control approach to the optical flow problem,
Systems & Control Letters,
Volume 87,
2016,
Pages 1-9,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115002054)
Abstract: The optical flow problem is reduced to an optimal control problem governed by a linear parabolic equation having the unknown velocity field (the optical flow) as drift term. This model is derived from a new assumption, that is, the brightness intensity is conserved on a moving pattern driven by a Gaussian stochastic process. The optimality conditions are deduced by a passage to the limit technique in an approximating optimal control problem introduced for a regularization purpose. Finally, the controller uniqueness is addressed.
Keywords: Optical flow; Gaussian process; Stochastic differential equations; Optimal control

Haris E. Psillakis,
An extension of the Georgiou–Smith example: Boundedness and attractivity in the presence of unmodelled dynamics via nonlinear PI control,
Systems & Control Letters,
Volume 92,
2016,
Pages 1-4,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691116000335)
Abstract: In this paper, a nonlinear extension of the Georgiou–Smith system is considered and robustness results are proved for a nonlinear PI controller with respect to fast parasitic first-order dynamics. More specifically, for a perturbed nonlinear system with sector bounded nonlinearity and unknown control direction, sufficient conditions for global boundedness and attractivity have been derived. It is shown that the closed loop system is globally bounded and attractive if (i) the unmodelled dynamics are sufficiently fast and (ii) the PI control gain has the Nussbaum function property. For the case of nominally unstable systems, the Nussbaum property of the control gain appears to be crucial. A simulation study confirms the theoretical results.
Keywords: Robustness; Nonlinear PI control; Nussbaum function


Editorial Board,
Systems & Control Letters,
Volume 92,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30019-6.
(http://www.sciencedirect.com/science/article/pii/S0167691116300196)


Editorial Board,
Systems & Control Letters,
Volume 85,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00196-6.
(http://www.sciencedirect.com/science/article/pii/S0167691115001966)

M.C. Tsakiris, D.C. Tarraf,
Algebraic decompositions of DP problems with linear dynamics,
Systems & Control Letters,
Volume 85,
2015,
Pages 46-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115001723)
Abstract: We consider Dynamic Programming (DP) problems in which the dynamics are linear, the cost is a function of the state, and the state-space is finite dimensional but defined over an arbitrary field. Starting from the natural decomposition of the state-space into a direct sum of invariant subspaces consistent with the rational canonical form, and assuming the cost functions exhibit an additive structure compatible with this decomposition, we extract from the original problem two distinct families of smaller DP problems associated with the invariant subspaces. Each family constitutes a decomposition of the original problem when the optimal policy and value function can be reconstructed from the optimal policies and value functions of the smaller problems. We derive necessary and sufficient conditions for these decompositions to exist, propose a readily verifiable sufficient condition for the first decomposition, and establish a hierarchy relating the two notions of decomposition.
Keywords: Dynamic programming; Decomposition; Rational canonical form

Sergey A. Timoshin,
Control system with hysteresis and delay,
Systems & Control Letters,
Volume 91,
2016,
Pages 43-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.008.
(http://www.sciencedirect.com/science/article/pii/S0167691116000372)
Abstract: A class of control-delay systems exhibiting a hysteresis behavior is considered. Existence of solutions and a relaxation result are obtained for this system.
Keywords: Evolution system; Delay; Hysteresis; Relaxation; Mixed controls

Shiyuan Lu, Zhiyun Lin, Ronghao Zheng, Gangfeng Yan,
Scheduling parallel Kalman filters with quantized deadlines,
Systems & Control Letters,
Volume 86,
2015,
Pages 9-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115001851)
Abstract: In this paper we explore the problem of scheduling parallel processes of Kalman filters to meet individual estimation error requirements. It is assumed that at each time-step measurements of only one process are received. We define real-time deadlines of transmissions and convert the problem into arranging sequence of tasks with corresponding deadlines. To reduce computations, cycles of transmissions are calculated and virtual processes are introduced into scheduling. A sliding window method is then designed to adjust the processes against real-time disturbances in applications. Compared with algorithms proposed in Lin and Wang (2013), the proposed algorithm is able to schedule a feasible sequence adaptively within a short scheduling window and requires little computation.
Keywords: Sensor scheduling; Kalman filtering; Parallel estimation; Periodic observation

Junjie Fu, Jinzhi Wang,
Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties,
Systems & Control Letters,
Volume 93,
2016,
Pages 1-12,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116000645)
Abstract: In this paper, we study the fixed-time coordinated tracking problem for second-order integrator systems with bounded input uncertainties. Two novel distributed controllers are proposed with which the convergence time of the tracking errors is globally bounded for any initial condition of the agents. When relative state measurements are available for each follower, an observer-based distributed control strategy is proposed which achieves fixed-time coordinated tracking for the perturbed second-order multi-agent systems. When only relative output measurements are available, uniform robust exact differentiators are employed together with the observer-based controller which is able to achieve fixed-time coordinated tracking with reduced measurements. Simulation examples are provided to demonstrate the performance of the proposed controllers.
Keywords: Multi-agent system; Coordinated tracking; Fixed-time; Second-order systems; Directed communication graph

Philippe Jouan, Saïd Naciri,
Convergence rate of nonlinear switched systems,
Systems & Control Letters,
Volume 87,
2016,
Pages 70-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115002145)
Abstract: This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of switching signals but not for all switching signals. We show that solutions corresponding to that class of switching signals converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for switching signals with a fixed dwell-time.
Keywords: Switched systems; Asymptotic stability; Weak Lyapunov functions; Convergence rate

Cristian Oară, Cristian Flutur, Marc Jungers,
Squaring down with zeros cancellation in generalized systems,
Systems & Control Letters,
Volume 92,
2016,
Pages 5-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.019.
(http://www.sciencedirect.com/science/article/pii/S0167691116000487)
Abstract: Squaring down with simultaneous zeros cancellation by series compensation of a general (possibly polynomial or improper) linear system is investigated. All static and dynamical compensators that spotlight minimal McMillan degree are parameterized. This general result is particularized to get compensators that preserve the L2 or L∞ norm of the original system, either in continuous or discrete-time. All results are completely general, numerically sound, and based on general realizations allowing for poles at infinity.
Keywords: Linear systems; Squaring down; Zeros cancellation; Compensation

Guofei Chai, Che Lin, Zhiyun Lin, Minyue Fu,
Single landmark based collaborative multi-agent localization with time-varying range measurements and information sharing,
Systems & Control Letters,
Volume 87,
2016,
Pages 56-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115002261)
Abstract: This paper considers the collaborative localization problem for a team of mobile agents. The goal is to estimate the relative coordinate of each agent with respect to a stationary landmark. Each agent is supposed to be able to measure its own velocity and the distances to nearby agents as well as the change rates of the distances. Due to limited sensing capability, movements of agents and possible interference of severe environments, the topology describing the measurements and communication information flow among the agents and the landmark is usually time-varying. Under such a scenario, this paper develops a consensus-like fusion scheme together with a continuous-time estimator for the collaborative localization problem. It is proved that the fused estimate of each agent’s position globally asymptotically converges to its true value if the movements of the agents satisfy a persistent excitation condition and each agent is uniformly jointly reachable from the landmark in the time-varying topology. The effectiveness of the proposed scheme is verified through simulations without and with measurement noises.
Keywords: Collaborative localization; Multi-agent systems; Switching topology; Consensus-like fusion

Emilia Fridman, Catherine Bonnet, Frederic Mazenc, Walid Djema,
Stability of the cell dynamics in acute myeloid leukemia,
Systems & Control Letters,
Volume 88,
2016,
Pages 91-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.006.
(http://www.sciencedirect.com/science/article/pii/S016769111500184X)
Abstract: In this paper we analyze the global asymptotic stability of the trivial solution for a multi-stage maturity acute myeloid leukemia model. By employing the positivity of the corresponding nonlinear time-delay model, where the nonlinearity is locally Lipschitz, we establish the global exponential stability under the same conditions that are necessary for the local exponential stability. The result is derived for the multi-stage case via a novel construction of linear Lyapunov functionals. In a simpler model of hematopoiesis (without fast self-renewal) our conditions guarantee also global exponential stability with a given decay rate. Moreover, in this simpler case the analysis of the PDE model is presented via novel Lyapunov functionals for the transport equations.
Keywords: Leukemia model; Time-delay systems; Positive systems; Transport equations; Lyapunov method


Editorial Board,
Systems & Control Letters,
Volume 89,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)00024-4.
(http://www.sciencedirect.com/science/article/pii/S0167691116000244)

Xiao-Heng Chang, Ju H. Park, Jianping Zhou,
Robust static output feedback H∞ control design for linear systems with polytopic uncertainties,
Systems & Control Letters,
Volume 85,
2015,
Pages 23-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115001735)
Abstract: This paper investigates the problem of robust static output feedback H∞ control for linear systems with polytopic uncertainties. A new method is proposed for robust static output feedback H∞ controller design. The proposed design method is applicable for general uncertain systems, without the need to impose any constraints on system matrices. The corresponding design conditions are presented in the form of linear matrix inequalities (LMIs). One of the advantages of the new method lies in its less conservatism. The proposed design method is also applicable to both continuous-time and discrete-time systems. The performance of the method is compared with other methods based on several examples.
Keywords: Linear systems; Polytopic uncertainties; Static output feedback H∞ controllers; Linear matrix inequalities (LMIs)

Christian Clason, Armin Rund, Karl Kunisch, Richard C. Barnard,
A convex penalty for switching control of partial differential equations,
Systems & Control Letters,
Volume 89,
2016,
Pages 66-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115002546)
Abstract: A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. The efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.
Keywords: Optimal control; Switching control; Partial differential equations; Nonsmooth optimization; Convex analysis; Semi-smooth Newton method


Editorial Board,
Systems & Control Letters,
Volume 88,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)00008-6.
(http://www.sciencedirect.com/science/article/pii/S0167691116000086)

Khalid Tourkey Atta, Andreas Johansson, Thomas Gustafsson,
On the stability analysis of phasor and classic extremum seeking control,
Systems & Control Letters,
Volume 91,
2016,
Pages 55-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116000360)
Abstract: In this work we present a semi-global practical asymptotic stability analysis for phasor extremum seeking control with a general non-linear dynamic system. With the same technique applied to the classic band pass filter algorithm, we present a more relaxed (less constrained) semi-global practical asymptotic stability condition compared to earlier work. The results are based on a non approximated averaging for both control techniques.
Keywords: Extremum seeking control; Phasor extremum seeking control; Semi-global practical asymptotic stability; Singular perturbation; Averaging

Zheming Wang, Chong-Jin Ong,
Distributed MPC of constrained linear systems with time-varying terminal sets,
Systems & Control Letters,
Volume 88,
2016,
Pages 14-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115002303)
Abstract: This paper proposes a decoupling strategy for the Distributed Model Predictive Control (DMPC) for a network of dynamically-coupled linear systems. Like most DMPC approaches, the proposed approach has a terminal set and uses a Lyapunov matrix for the terminal cost in the online optimization problem for each system. Unlike them, the terminal set changes at every time step and the Lyapunov matrix is not block-diagonal. These features result in a less conservative DMPC formulation. The proposed method is easy to implement when the network is strongly connected (or when a central collector is used). Otherwise, the computations of the terminal set require the online solutions of a series of linear programming problems but can be speeded up significantly by preprocessing. Numerical examples showing these results are provided.
Keywords: Distributed Model Predictive Control; Time-varying terminal sets

Haili Liang, Ming Cao, Xiaofan Wang,
Analysis and shifting of stochastically stable equilibria for evolutionary snowdrift games,
Systems & Control Letters,
Volume 85,
2015,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115001577)
Abstract: In this paper we investigate the stochastic stability of evolutionary snowdrift games, which belong to a class of standard games popular in theoretical biology for the study of the mechanism of the emergence and maintenance of cooperation in large populations of strategically interacting individuals. We identify stochastically stable equilibria for two-player and multi-player evolutionary snowdrift games, for which the existing results are almost exclusively on the former. For the two cases with the same values of cost and benefit of cooperation, we show that like the two-player case, under certain conditions, there is a unique stochastically stable equilibrium in the multi-player case, at which, however, the proportion of cooperators can be higher than that of the two-player case. More importantly, the proportion of cooperators can be manipulated as the stochastically stable equilibrium is being shifted by changing the game parameters. So the results indicate a promising approach to controlling the proportion of cooperators in large populations that has not been reported before. Besides theoretical analysis, we demonstrate our results through numerical computations and simulations as well.
Keywords: Evolutionary games; Stochastic stability; Cooperation vs defection

Carlos J. Braga Barros, Victor H.L. Rocha,
Attraction and Lyapunov stability for control systems on vector bundles,
Systems & Control Letters,
Volume 92,
2016,
Pages 28-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116000359)
Abstract: Let π:E→B be a finite-dimensional vector bundle whose base space is compact. In this paper, we study attraction and Lyapunov stability for control systems on E. We prove that, under certain conditions, the concepts of Conley attractor, uniform attractor, attractor, exponential attractor, asymptotically stable set and stable set are equivalent for the zero section of π:E→B.
Keywords: Attraction; Lyapunov stability; Control systems; Vector bundles

Andrii Mironchenko,
Local input-to-state stability: Characterizations and counterexamples,
Systems & Control Letters,
Volume 87,
2016,
Pages 23-28,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.014.
(http://www.sciencedirect.com/science/article/pii/S0167691115002157)
Abstract: We show that a nonlinear locally uniformly asymptotically stable infinite-dimensional system is automatically locally input-to-state stable (LISS) provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs. Also we prove that LISS is equivalent to existence of a LISS Lyapunov function. We show by means of a counterexample that if this uniformity is not present, then the equivalence of local asymptotic stability and local ISS does not hold anymore. Using a modification of this counterexample we show that in infinite dimensions a uniformly globally asymptotically stable at zero, globally stable and locally ISS system possessing an asymptotic gain property does not have to be ISS (in contrast to finite dimensional case).
Keywords: Nonlinear control systems; Infinite-dimensional systems; Input-to-state stability; Lyapunov methods

Felipe Núñez, Yongqiang Wang, Andrew R. Teel, Francis J. Doyle,
Synchronization of pulse-coupled oscillators to a global pacemaker,
Systems & Control Letters,
Volume 88,
2016,
Pages 75-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115002431)
Abstract: Pulse-coupled oscillators (PCOs) are limit cycle oscillators coupled by exchanging pulses at discrete time instants. Their importance in biology and engineering has motivated numerous studies aiming to understand the basic synchronization properties of a network of PCOs. In this work, we study synchronization of PCOs subject to a global pacemaker (or global cue) and local interactions between slave oscillators. We characterize solutions and give synchronization conditions using the phase response curve (PRC) as the design element, which is restricted to be of the delay type in the first half of the cycle, interval (0,π), and of the advance type in the second half of the cycle, interval (π,2π). It is shown that global synchronization is feasible when using an advance-delay PRC if the influence of the global cue is strong enough. Numerical examples are provided to illustrate the analytical findings.
Keywords: Pulse-coupled oscillators; Synchronization; Phase models; Phase response curve

Vivek S. Borkar, Raaz Dwivedi, Neeraja Sahasrabudhe,
Gaussian approximations in high dimensional estimation,
Systems & Control Letters,
Volume 92,
2016,
Pages 42-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.001.
(http://www.sciencedirect.com/science/article/pii/S016769111600058X)
Abstract: Several estimation techniques assume validity of Gaussian approximations for estimation purposes. Interestingly, these ensemble methods have proven to work very well for high-dimensional data even when the distributions involved are not necessarily Gaussian. We attempt to bridge the gap between this oft-used computational assumption and the theoretical understanding of why this works, by employing some recent results on random projections on low dimensional subspaces and concentration inequalities.
Keywords: Gaussian approximations; High dimensional estimation; Log-concave distributions; Stochastic sparsity; Random projections

Dabo Xu, Xinghu Wang, Yiguang Hong, Zhong-Ping Jiang,
Global robust distributed output consensus of multi-agent nonlinear systems: An internal model approach,
Systems & Control Letters,
Volume 87,
2016,
Pages 64-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.11.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115002273)
Abstract: This paper studies the problem of global robust distributed output consensus of heterogeneous leader–follower multi-agent nonlinear systems by general directed output interactions. For a class of minimum-phase single-input single-output nonlinear agents having unity relative degree, it is shown that the problem is solvable by an internal model approach under certain mild conditions. A Lyapunov function based output-feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network.
Keywords: Nonlinear systems; Multi-agent systems; Consensus; Distributed stabilization

Yuan-Hua Ni, Xun Li, Ji-Feng Zhang,
Mean-field stochastic linear–quadratic optimal control with Markov jump parameters,
Systems & Control Letters,
Volume 93,
2016,
Pages 69-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.04.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116300172)
Abstract: This paper considers a class of mean-field stochastic linear–quadratic optimal control problems with Markov jump parameters. The new feature of these problems is that means of state and control are incorporated into the systems and the cost functional. Based on the modes of Markov chain, the corresponding decomposition technique of augmented state and control is introduced. It is shown that, under some appropriate conditions, there exists a unique optimal control, which can be explicitly given via solutions of two generalized difference Riccati equations. A numerical example sheds light on the theoretical results established.
Keywords: Mean-field; Markov jump; Stochastic control


Editorial Board,
Systems & Control Letters,
Volume 91,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(16)30005-6.
(http://www.sciencedirect.com/science/article/pii/S0167691116300056)

S. Mou, Z. Lin, L. Wang, D. Fullmer, A.S. Morse,
A distributed algorithm for efficiently solving linear equations and its applications (Special Issue JCW),
Systems & Control Letters,
Volume 91,
2016,
Pages 21-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.010.
(http://www.sciencedirect.com/science/article/pii/S0167691116000396)
Abstract: A distributed algorithm is proposed for solving a linear algebraic equation Ax=b over a multi-agent network, where A∈Rn̄×n and the equation has a unique solution x∗∈Rn. Each agent knows only a subset of the rows of [Ab], controls a state vector xi(t) of size smaller than n and is able to receive information from its nearby neighbors. Neighbor relations are characterized by time-dependent directed graphs. It is shown that for a large class of time-varying networks, the proposed algorithm enables each agent to recursively update its own state by only using its neighbors’ states such that all xi(t) converge exponentially fast to a specific part of x∗ of interest to agent i. Applications of the proposed algorithm include solving the least square solution problem and the network localization problem.
Keywords: Distributed algorithms; Least-square solution; Network localization

Zhi-Liang Zhao, Bao-Zhu Guo,
Extended state observer for uncertain lower triangular nonlinear systems,
Systems & Control Letters,
Volume 85,
2015,
Pages 100-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115001826)
Abstract: The extended state observer (ESO) is a key part of the active disturbance rejection control approach, a new control strategy in dealing with large uncertainty. In this paper, a nonlinear ESO is designed for a kind of lower triangular nonlinear systems with large uncertainty. The uncertainty may come from unmodeled system dynamics and external disturbance. We first investigate a nonlinear ESO with high constant gain and present a practical convergence. Two types of ESO are constructed with explicit error estimations. Secondly, a time varying gain ESO is proposed for reducing peaking value near the initial time caused by constant high gain approach. The numerical simulations are presented to show visually the peaking value reduction. The mechanism of peaking value reduction by time varying gain approach is analyzed.
Keywords: Extended state observer; Nonlinear systems; Uncertainty

Kamil A. Khan, Paul I. Barton,
Switching behavior of solutions of ordinary differential equations with abs-factorable right-hand sides,
Systems & Control Letters,
Volume 84,
2015,
Pages 27-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.007.
(http://www.sciencedirect.com/science/article/pii/S016769111500153X)
Abstract: We consider nonsmooth dynamic systems that are formulated as the unique solutions of ordinary differential equations (ODEs) with right-hand side functions that are finite compositions of analytic functions and absolute-value functions. Various non-Zenoness results are obtained for such solutions: in particular, any absolute-value function in the ODE right-hand side can only switch between its two linear pieces finitely many times on any finite duration, even when a discontinuous control input is included. These results are extended to obtain numerically verifiable necessary conditions for the emergence of “valley-tracing modes”, in which the argument of an absolute-value function is identically zero for a nonzero duration. Such valley-tracing modes can create theoretical and numerical complications during sensitivity analysis or optimization. We show that any valley-tracing mode must begin either at the initial time, or when another absolute-value function switches between its two linear pieces.
Keywords: Ordinary differential equations; Nonsmooth analysis; Switching systems; Non-Zeno behavior

Ali A. Zaidi, Serdar Yüksel, Tobias J. Oechtering, Mikael Skoglund,
On the tightness of linear policies for stabilization of linear systems over Gaussian networks,
Systems & Control Letters,
Volume 88,
2016,
Pages 32-38,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115001942)
Abstract: In this paper, we consider stabilization of multi-dimensional linear systems driven by Gaussian noise controlled over parallel Gaussian channels. For such systems, it has been recognized that for stabilization in the sense of asymptotic stationarity or stability in probability, Shannon capacity of a channel is an appropriate measure on characterizing whether a system can be made stable when controlled over the channel. However, this is in general not the case for quadratic stabilization. On a related problem of joint-source channel coding, in the information theory literature, the source-channel matching principle has been shown to lead to optimality of uncoded or analog transmission and when such matching conditions occur, it has been shown that capacity is also a relevant figure of merit for quadratic stabilization. A special case of this result is applicable to a scalar LQG system controlled over a scalar Gaussian channel. In this paper, we show that even in the absence of source-channel matching, to achieve quadratic stability, it may suffice that information capacity (in Shannon’s sense) is greater than the sum of the logarithm of unstable eigenvalue magnitudes. In particular, we show that periodic linear time varying coding policies are optimal in the sense of obtaining a finite second moment for the state of the system with minimum transmit power requirements for a large class of vector Gaussian channels. Our findings also extend the literature which has considered noise-free systems.
Keywords: Networked control systems; Gaussian channels; Channel capacity; Stabilization

Feng Xiao, Tongwen Chen,
Sampled-data consensus in multi-agent systems with asynchronous hybrid event-time driven interactions,
Systems & Control Letters,
Volume 89,
2016,
Pages 24-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115002479)
Abstract: This paper investigates sampled-data consensus in an undirected network of multiple integrators and characterizes the effectiveness of a hybrid event-time driven consensus protocol in different asynchronous scheduling schemes of event detection in terms of interaction topology, asynchronous matrix, and time delays. The proposed hybrid driven protocol has the benefit of guaranteed performance at reduced communication and computation costs and has robustness against interaction/event-detection time delays. Furthermore, the obtained results are still valid in many other practical situations, such as sampled-data consensus with measurement errors and quantized consensus.
Keywords: Multi-agent systems; Sampled-data consensus; Asynchronous consensus; Time delays

Ivo Herman, Dan Martinec, J.J.P. Veerman,
Transients of platoons with asymmetric and different Laplacians,
Systems & Control Letters,
Volume 91,
2016,
Pages 28-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.013.
(http://www.sciencedirect.com/science/article/pii/S0167691116000426)
Abstract: We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, an optimization-based procedure is used to find the controller properties.
Keywords: Vehicular platoons; Different asymmetries; Distributed control; Scaling; Multiple Laplacian

Timo Reis, Matthias Voigt,
The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions,
Systems & Control Letters,
Volume 86,
2015,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115001796)
Abstract: The Kalman–Yakubovich–Popov lemma is a central result in systems and control theory which relates the positive semidefiniteness of a Popov function on the imaginary axis to the solvability of a linear matrix inequality. In this paper we prove sufficient conditions for the existence of a nonpositive solution of this inequality for differential-algebraic systems. Our conditions are given in terms of positivity of a modified Popov function in the right complex half-plane. Our results also apply to non-controllable systems. Consequences of our results are bounded real and positive real lemmas for differential-algebraic systems.
Keywords: Differential-algebraic equation; Kalman–Yakubovich–Popov lemma; Popov function; Bounded real lemma; Positive real lemma

Anantharaman Subbaraman, Andrew R. Teel,
On the equivalence between global recurrence and the existence of a smooth Lyapunov function for hybrid systems,
Systems & Control Letters,
Volume 88,
2016,
Pages 54-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115001553)
Abstract: We study a weak stability property called recurrence for a class of hybrid systems. An open set is recurrent if there are no finite escape times and every complete trajectory eventually reaches the set. Under sufficient regularity properties for the hybrid system we establish that the existence of a smooth, radially unbounded Lyapunov function that decreases along solutions outside an open, bounded set is a necessary and sufficient condition for recurrence of that set. Recurrence of open, bounded sets is robust to sufficiently small state dependent perturbations and this robustness property is crucial for establishing the existence of a Lyapunov function that is smooth. We also highlight some connections between recurrence and other well studied properties like asymptotic stability and ultimate boundedness.
Keywords: Recurrence; Converse theorem; Ultimate boundedness; Hybrid systems; Robust recurrence

Christoph Kawan,
On the structure of uniformly hyperbolic chain control sets,
Systems & Control Letters,
Volume 90,
2016,
Pages 71-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.018.
(http://www.sciencedirect.com/science/article/pii/S0167691116000025)
Abstract: The following theorem is proved: Let Q be an isolated compact chain control set of a control-affine system on a smooth manifold M. If Q is uniformly hyperbolic without center bundle, then the lift of Q to the extended state space U×M, where U is the space of control functions, is a graph over U. In other words, for every control u∈U there is a unique x∈Q such that the corresponding state trajectory φ(t,x,u) evolves in Q.
Keywords: Nonlinear control; Control-affine system; Chain control set; Uniform hyperbolicity

E. Fernández-Cara, J. Limaco, S.B. de Menezes,
On the controllability of a free-boundary problem for the 1D heat equation,
Systems & Control Letters,
Volume 87,
2016,
Pages 29-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115002121)
Abstract: This paper deals with the local null control of a free-boundary problem for the classical 1D heat equation with distributed controls, locally supported in space. In the main result we prove that, if the final time T is fixed and the initial state is sufficiently small, there exist controls that drive the state exactly to rest at time t=T.
Keywords: Null controllability; Free-boundary problems; 1D heat equation; Carleman estimates

Jiangshuai Huang, Changyun Wen, Wei Wang, Yong-Duan Song,
Global stable tracking control of underactuated ships with input saturation,
Systems & Control Letters,
Volume 85,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115001395)
Abstract: In this paper, tracking control of underactuated ship in the presence of input saturation is addressed. By dividing the tracking error dynamic system into a cascade of two subsystems, the torques in surge and yaw axes are designed separately using the backstepping technique. More specifically, we design the yaw axis torque in such a way that its corresponding subsystem is finite time stable, which makes it to be de-coupled from the second subsystem after a finite time. This enables us to design the torque in the surge axis independently. It is shown that the closed-loop system is stable and the mean-square tracking errors can be made arbitrarily small by choosing design parameters. Simulation results also verify the effectiveness of the proposed scheme.
Keywords: Tracking control; Underactuated ships; Input saturation

Chuanrui Wang, Xinghu Wang, Haibo Ji,
Leader-following consensus for a class of second-order nonlinear multi-agent systems,
Systems & Control Letters,
Volume 89,
2016,
Pages 61-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115002480)
Abstract: This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.
Keywords: Multi-agent systems; Distributed control; Nonlinear systems; Directed topology

J.Y. Kaminski, R. Shorten, E. Zeheb,
Exact stability test and stabilization for fractional systems,
Systems & Control Letters,
Volume 85,
2015,
Pages 95-99,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.005.
(http://www.sciencedirect.com/science/article/pii/S016769111500170X)
Abstract: In this paper we point out a connection between regular chains and the stability of fractional order systems. This observation leads to an elementary test for the stability of commensurate fractional systems.
Keywords: Fractional order systems; Stability; Regular chains algorithms

M. Sassano, L. Zaccarian,
Model recovery anti-windup for output saturated SISO linear closed loops,
Systems & Control Letters,
Volume 85,
2015,
Pages 109-117,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115001838)
Abstract: We define model recovery anti-windup for SISO linear control systems with output saturation. We address the problem by relying on a hybrid modification of the linear closed loop which employs a suitable logic variable to activate/deactivate various components of a control scheme. The scheme relies on a finite-time observation law, an open-loop observer and an open-loop input generator which is capable of driving the plant output within the saturation limits. Then the control scheme is based on suitable (hybrid) resetting laws allowing the controller to operate on the artificial output signal generated by the open-loop observer when the actual plant output is outside the saturation limits. Unlike existing results, not only we prove uniform global asymptotic stability of the closed loop, but we also prove the local preservation and global recovery properties, typical of model recovery anti-windup paradigms. We also illustrate the proposed technique on an example study.
Keywords: Output saturation; Hybrid systems; Anti-windup scheme

Yunliang Wei, Wei Xing Zheng, Shengyuan Xu,
Anti-disturbance control for nonlinear systems subject to input saturation via disturbance observer,
Systems & Control Letters,
Volume 85,
2015,
Pages 61-69,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115001711)
Abstract: This paper is concerned with the problem of the disturbance observer based control for a class of continuous-time uncertain systems subject to input saturation and nonlinearity. The input of the system includes two parts, the control input and the disturbance input. The nonlinearity of the system, which satisfies a global Lipschitz condition, is considered as two cases of known nonlinearity and unknown nonlinearity. By virtue of the technique of the disturbance observer based controller, the anti-disturbance controllers are designed respectively with both the polytopic and dead-zone representations of the saturation function, which ensure that the resulting closed-loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the Lyapunov function. Further, an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states. An example of application design for a flight control system illustrates the effectiveness of the proposed results.
Keywords: Disturbance uncertainties; Disturbance observer based control; Disturbance attenuation; Input saturation

Jingying Ma, Yuanshi Zheng, Long Wang,
Topology selection for multi-agent systems with opposite leaders,
Systems & Control Letters,
Volume 93,
2016,
Pages 43-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.007.
(http://www.sciencedirect.com/science/article/pii/S0167691116000657)
Abstract: For the multi-agent system with a navigational leader and its opponent, the followers cannot converge to the state of the navigational leader. In this paper, we consider the topology selection problem to minimize the opponent’s influence which is measured by the tracking error of the system. Firstly, two combinatorial optimization problems are formulated. One is to minimize the tracking error by selecting guided informed-agents (the followers who can obtain the navigational leader’s information). The other is to choose minimal number of guided informed-agents under an upper bound constraint of the tracking error. Secondly, for the scenario where the guided informed-agents are preset, we consider the problem of assigning the weights of edges to minimize the tracking error. Three convex optimization problems are proposed to evaluate the upper and lower bounds of the tracking error. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.
Keywords: Multi-agent systems; Tracking; Topology selection

Vinayaka G. Yaji, Shalabh Bhatnagar,
Necessary and sufficient conditions for optimality in constrained general sum stochastic games,
Systems & Control Letters,
Volume 85,
2015,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115001565)
Abstract: In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium.
Keywords: Constrained Markov games; Stationary Nash equilibrium; Linear programs; Discounted and average cost/reward settings

Daniel Viegas, Pedro Batista, Paulo Oliveira, Carlos Silvestre,
On the stability of the continuous-time Kalman filter subject to exponentially decaying perturbations,
Systems & Control Letters,
Volume 89,
2016,
Pages 41-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115002133)
Abstract: This paper details the stability analysis of the continuous-time Kalman filter dynamics for linear time-varying systems subject to exponentially decaying perturbations. It is assumed that estimates of the input, output, and matrices of the system are available, but subject to unknown perturbations which decay exponentially with time. It is shown that if the nominal system is uniformly completely observable and uniformly completely controllable, and if the state, input, and matrices of the system are bounded, then the Kalman filter built using the perturbed estimates is a suitable state observer for the nominal system, featuring exponentially convergent error dynamics.
Keywords: Kalman filtering; Estimation; Time-varying systems

Junyong Sun, Zhiyong Geng, Yuezu Lv,
Adaptive output feedback consensus tracking for heterogeneous multi-agent systems with unknown dynamics under directed graphs,
Systems & Control Letters,
Volume 87,
2016,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.007.
(http://www.sciencedirect.com/science/article/pii/S016769111500208X)
Abstract: This paper considers the distributed consensus tracking problem for the linear multi-agent systems with unknown dynamics under general directed graphs. Based on the output information among the agents, distributed adaptive consensus tracking protocols together with two observers, consisting of a local observer and an adaptive estimator, are designed to guarantee that all the signals in the closed-loop dynamics are uniformly ultimately bounded and the tracking errors converge to a small neighborhood around the origin. Moreover, the consensus protocols are in fully distributed fashion in the sense that the coupling gains in the controllers are independent without requiring the global knowledge that the eigenvalues of the Laplacian matrix associated with the whole communication graph. Finally, a simulation example is provided to verify the theoretical results.
Keywords: Cooperative control; Output feedback; Adaptive control; Multi-agent system; Directed graph

Andreea Röthig, Jürgen Adamy,
On stabilizing linear systems with input saturation via soft variable structure control laws,
Systems & Control Letters,
Volume 89,
2016,
Pages 47-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115002492)
Abstract: A large number of control methods deal with stabilizing single-input linear systems with input saturation. The linear full-state feedback is one of the most used, yielding either nonsaturating or high gain controls, whereby the saturating effects of the latter are reduced by means of anti-windup structures. Among the nonlinear controls, the time optimal control, in this case a bang–bang type control, yields the fastest time response, but its switching surface is generally not characterizable. Related to the speed of the time response is the convergence rate, which can be determined using invariant sets. The most used ones are the ellipsoidal sets, since they can be analyzed using powerful tools such as the Lyapunov equation and designed via convex optimization. For this reason, they are also used for designing soft variable structure controls. The paper presents a nonconservative design method for a stabilizing control of this type employing implicit Lyapunov functions (iLF). A nonsaturating control law is given, including some infinitely densely nested and contractive invariant sets of the equilibrium state. The control law is then optimized by maximizing the iLF-based lower bound of the convergence rate. The maximal convergence control is shown to be of bang–bang type, with a parameter dependent switching scheme. To overcome possible difficulties of a switching controller, a saturating high gain control is also presented.
Keywords: Single-input LTI-systems; Actuator saturation; Finslers’ lemma; Implicit Lyapunov function; Contractive invariance; Convergence rate; Linear matrix inequalities

Mei Liu, Junlin Xiong,
On non-proper negative imaginary systems,
Systems & Control Letters,
Volume 88,
2016,
Pages 47-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115002091)
Abstract: This paper studies non-proper negative imaginary systems. First, the concept of negative imaginary transfer functions that may have poles at the origin and infinity is introduced. Then, a generalized lemma is presented to provide a sufficient condition to characterize the non-proper negative imaginary properties of systems. The generalized lemma is given in terms of complex variable s in the quarter domain of analyticity. Compared to previous results, our result removes the symmetric restriction. Also, a new relationship is established between (lossless) negative imaginary and (lossless) positive real transfer function matrices by using a minor decomposition. The results in this paper give us the possibility to address non-proper and non-symmetric descriptor systems with negative imaginary frequency response. Several examples are presented to illustrate the results.
Keywords: Negative imaginary systems; Non-proper transfer functions; Generalized lemmas; Positive real systems

Márcio F. Braga, Cecília F. Morais, Eduardo S. Tognetti, Ricardo C.L.F. Oliveira, Pedro L.D. Peres,
Discretization and event triggered digital output feedback control of LPV systems,
Systems & Control Letters,
Volume 86,
2015,
Pages 54-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115001929)
Abstract: This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.
Keywords: Discretized linear systems; Networked control systems; Taylor series expansion; Output feedback control; Time varying parameters; Linear matrix inequalities

Li Deng, Zhifei Zhang,
Controllability for transmission wave/plate equations on Riemannian manifolds,
Systems & Control Letters,
Volume 91,
2016,
Pages 48-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.016.
(http://www.sciencedirect.com/science/article/pii/S0167691116000451)
Abstract: In this paper we consider controllability for transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. We show that such a system is exactly controllable by boundary controls only along the exterior boundary, which means there is no control on the interface of the transmission system. Our proofs rely on the Hilbert Uniqueness Method (HUM) and geometric multiplier method.
Keywords: Exact controllability; Transmission problem; Riemannian geometry method

Bujar Gashi,
Stochastic minimum-energy control,
Systems & Control Letters,
Volume 85,
2015,
Pages 70-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115001802)
Abstract: We give the solution to the minimum-energy control problem for linear stochastic systems. The problem is as follows: given an exactly controllable system, find the control process with the minimum expected energy that transfers the system from a given initial state to a desired final state. The solution is found in terms of a certain forward–backward stochastic differential equation of Hamiltonian type.
Keywords: Exact controllability; Minimum-energy control; Hamiltonian system

Lars Grüne, Matthias A. Müller,
On the relation between strict dissipativity and turnpike properties,
Systems & Control Letters,
Volume 90,
2016,
Pages 45-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116000177)
Abstract: For discrete time nonlinear systems we study the relation between strict dissipativity and so called turnpike-like behavior in optimal control. Under appropriate controllability assumptions we provide several equivalence statements involving these two properties. The relation of strict dissipativity to an exponential variant of the turnpike property is also studied.
Keywords: Strict dissipativity; Turnpike property; Discrete time optimal control

Joonho Lee, Ranjan Mukherjee, Hassan K. Khalil,
Output feedback performance recovery in the presence of uncertainties,
Systems & Control Letters,
Volume 90,
2016,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.016.
(http://www.sciencedirect.com/science/article/pii/S0167691116000050)
Abstract: We propose an output-feedback tracking controller for uncertain, nonaffine, nonlinear systems. The output feedback controller results in a closed-loop system with a three-time-scale structure; an extended high-gain observer estimates unmeasured states and uncertainties in the fastest time scale and dynamic inversion is used to deal with nonaffine inputs and input uncertainties in the intermediate time scale while the plant dynamics evolves in the slowest time scale. The dynamic inversion algorithm is based on sector conditions and results in exponential convergence of the inputs. Together with the extended high-gain observer, dynamic inversion results in performance recovery of a target system. The singular perturbation method is used to analyze the stability and performance of the system and numerical simulations are used to demonstrate the effectiveness of the control design.
Keywords: Extended high-gain observers; Dynamic inversion; Uncertain nonlinear systems; Performance recovery

Gildas Besançon, Iulian Munteanu,
Control strategy for state and input observer design,
Systems & Control Letters,
Volume 85,
2015,
Pages 118-122,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115001887)
Abstract: In this note, an alternative to classical methods for observer design is discussed, based on a dual control approach: it is indeed highlighted how an observer (at least approximate) can be obtained for a system by designing a control law for an auxiliary copy of this system, so that it tracks the system output. An important ingredient in this approach is the use of high-gain in the control design. The strategy is illustrated by various examples, including the case of unknown input reconstruction.
Keywords: State observer; Input observer; High-gain control; Nonlinear systems

Yuchun Li, Sean Phillips, Ricardo G. Sanfelice,
Basic properties and characterizations of incremental stability prioritizing flow time for a class of hybrid systems,
Systems & Control Letters,
Volume 90,
2016,
Pages 7-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.015.
(http://www.sciencedirect.com/science/article/pii/S016769111500256X)
Abstract: This paper introduces incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints. The specific class of hybrid systems considered are those that do not have consecutive jumps nor Zeno behavior. The notion of incremental asymptotic stability is used to describe the behavior of the distance between every pair of solutions to the system having stable behavior (incremental stability) and approaching zero asymptotically (incremental attractivity). A version of this notion that is uniform (in hybrid time) with respect to initial conditions is also introduced. These notions prioritize flow time and are illustrated in examples. Basic properties of the class of systems are considered and those implied by the new notions are revealed. An equivalence characterization of the uniform notion is provided in terms of a KL-function. Moreover, sufficient and necessary conditions under which asymptotic stability implies the new incremental notions are provided. We consider the case when the original hybrid system has an asymptotically stable compact set and also the case when an auxiliary hybrid system, which has twice the dimension of the original system, has a diagonal-like set asymptotically stable.
Keywords: Hybrid systems; Incremental stability; Asymptotic stability

A.I.G. Vardulakis, C. Kazantzidou,
Proper, denominator assigning feedback compensators equivalent to state variable feedback,
Systems & Control Letters,
Volume 89,
2016,
Pages 35-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115002467)
Abstract: For linear, time-invariant, stabilizable multivariable systems, we examine the problem of the existence and computation of proper denominator assigning and internally stabilizing feedback compensators, which give rise to a closed-loop system, whose transfer function matrix is equal to one that can be obtained by the action of state variable feedback. We establish a sufficient condition for the solution of this problem for the class of systems with the same number of inputs and outputs and non-singular transfer function matrix with all its zeros located in the open left half of the complex plane.
Keywords: Denominator assignment; Euclidean algorithm; Proper feedback compensators; State feedback

Khalid Tourkey Atta, Andreas Johansson, Thomas Gustafsson,
Extremum seeking control based on phasor estimation,
Systems & Control Letters,
Volume 85,
2015,
Pages 37-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115001772)
Abstract: We present an extremum seeking control algorithm based on the estimation of the phasor of the perturbation frequency in the output of the plant. The phasor estimator is based on a continuous time Kalman filter, which is reduced into a variable gain observer by explicitly solving the special case of the Riccati equation. Local stability of the proposed algorithm for general non-linear dynamic systems using averaging and singular perturbations is presented for the single input case. The advantage of the presented algorithm is that it can be used on plants with large and even variable phase lag.
Keywords: Extremum seeking control; Phasor estimation; Local stability analysis

Vladimir Yu. Protasov,
Linear switching systems with slow growth of trajectories,
Systems & Control Letters,
Volume 90,
2016,
Pages 54-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.006.
(http://www.sciencedirect.com/science/article/pii/S0167691116000207)
Abstract: We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon is proved to be impossible in dimension 2, while in all bigger dimensions the sublinear growth may occur. The corresponding examples are provided and several open problems are formulated.
Keywords: Dynamical systems; Linear switching systems; Growth of trajectories; Stability; Resonance

Xinmin Song, Ju H. Park,
Linear quadratic regulation problem for discrete-time systems with multi-channel multiplicative noise,
Systems & Control Letters,
Volume 89,
2016,
Pages 74-82,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.017.
(http://www.sciencedirect.com/science/article/pii/S0167691115002583)
Abstract: This paper investigates the linear quadratic regulation (LQR) problem for discrete-time systems with multiplicative noise. Multiplicative noise is usually assumed to be a scalar in existing literature works. Motivated by recent applications of networked control systems and MIMO communication technology, we consider multi-channel multiplicative noise represented by a diagonal matrix. We first show that the finite horizon LQR problem can be solved using a generalized Riccati equation. We then prove the convergence of the generalized Riccati equation under the conditions of stabilization and exact observability, and obtain the solution to the infinite horizon LQR problem. Finally, we provide a numerical example to demonstrate the proposed approach.
Keywords: Multi-channel; Generalized Riccati equation; LQR; Multiplicative noise; Convergence

Jiao Li, Jun Zhao, Chao Chen,
Dissipativity and feedback passivation for switched discrete-time nonlinear systems,
Systems & Control Letters,
Volume 87,
2016,
Pages 47-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115002066)
Abstract: This paper studies dissipativity for switched discrete-time nonlinear systems using multiple storage functions and multiple supply rates. A sufficient condition for dissipativity of the switched nonlinear system is given under some switching law. Then, the result is extended to find a condition under which a switched system is feedback equivalent to a passive switched system. Switched passivity condition and switched l2-gain inequalities are, respectively, given, which are generalizations of the classical ones. Furthermore, the assumption of zero dynamics having passivity is relaxed. Passivity is also shown to be preserved under feedback interconnection.
Keywords: Switched systems; Switching law; Dissipativity; Multiple supply rates; Feedback passivation; l2-gain


Editorial Board,
Systems & Control Letters,
Volume 87,
2016,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00234-0.
(http://www.sciencedirect.com/science/article/pii/S0167691115002340)

Prashanth L.A., Prasad H.L., Shalabh Bhatnagar, Prakash Chandra,
A constrained optimization perspective on actor–critic algorithms and application to network routing,
Systems & Control Letters,
Volume 92,
2016,
Pages 46-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.020.
(http://www.sciencedirect.com/science/article/pii/S0167691116000566)
Abstract: We propose a novel actor–critic algorithm with guaranteed convergence to an optimal policy for a discounted reward Markov decision process. The actor incorporates a descent direction that is motivated by the solution of a certain non-linear optimization problem. We also discuss an extension to incorporate function approximation and demonstrate the practicality of our algorithms on a network routing application.
Keywords: Actor–critic algorithm; Reinforcement learning; Constrained optimization

Yongchao Man, Yungang Liu,
Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems,
Systems & Control Letters,
Volume 90,
2016,
Pages 20-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.09.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116000049)
Abstract: This paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.
Keywords: Nonlinear systems; Unmeasured states dependent growth; Serious unknowns and time-variations; Additive input disturbance; Output-feedback; Time-varying method; Adaptive technique


Editorial Board,
Systems & Control Letters,
Volume 86,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00218-2.
(http://www.sciencedirect.com/science/article/pii/S0167691115002182)

Daniel Vizer, Guillaume Mercère, Olivier Prot, Edouard Laroche,
H∞-norm-based optimization for the identification of gray-box LTI state-space model parameters,
Systems & Control Letters,
Volume 92,
2016,
Pages 34-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.03.003.
(http://www.sciencedirect.com/science/article/pii/S0167691116000608)
Abstract: In this paper, the challenging problem of determining the unknown parameters of an identifiable LTI state-space representation of a stable system is addressed by resorting to a specific H∞-norm-based optimization algorithm. More specifically, by assuming the availability of a reliable fully-parameterized representation of the system to identify, the algorithm developed herein consists in restructuring this initial black-box representation of the system dynamics via the optimization of a dedicated maximum eigenvalue-based criterion. This study shows that this H∞-norm-based approach can be seen as a good solution for the identification of gray-box LTI state-space representations and, by extension, as an interesting alternative or a reliable initialization step for the standard output-error techniques.
Keywords: System identification; H∞-norm; Non-smooth optimization; Gray-box model; Parameterization

Xu Jin,
Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking,
Systems & Control Letters,
Volume 89,
2016,
Pages 16-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115002509)
Abstract: In this work, we present a new distributed adaptive iterative learning control (AILC) scheme for a class of high-order nonlinear multi-agent systems (MAS) under alignment condition with both parametric and nonparametric system uncertainties, where the actuators may be faulty and the control input gain functions are not fully known. Backstepping design with the composite energy function (CEF) structure is used in the discussion. Through rigorous analysis, we show that under this new AILC scheme, uniform convergence of agents output tracking error over the iteration domain is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed AILC scheme.
Keywords: Consensus; Adaptive iterative learning control; Fault tolerant; Multi-agent system; Nonlinear system

Marcos G. Todorov, Marcelo D. Fragoso,
New methods for mode-independent robust control of Markov jump linear systems,
Systems & Control Letters,
Volume 90,
2016,
Pages 38-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691116000165)
Abstract: This paper treats the H2 and H∞ controls of linear systems with Markov jump disturbances, via new design methods based on linear matrix inequalities (LMIs). The proposed techniques are especially tailored to the scenario where the jump process cannot be measured, and apply to homogeneous Markov chains of any structure. In the scenario of polytopic uncertainty affecting the system matrices, new uncertainty-dependent methods are introduced for the design of robust controllers. Several numerical examples illustrate situations where the proposed techniques are less conservative than the ones found in the literature.
Keywords: Robust control; Markov chain; Partial observations

Xingye Zhang, Jesse B. Hoagg,
Frequency-domain subsystem identification with application to modeling human control behavior,
Systems & Control Letters,
Volume 87,
2016,
Pages 36-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115002108)
Abstract: We present a frequency-domain subsystem identification algorithm that identifies unknown feedback and feedforward subsystems that are interconnected with a known subsystem. This method requires only accessible input and output measurements, applies to linear time-invariant subsystems, and uses a candidate-pool approach to ensure asymptotic stability of the identified closed-loop transfer function. We analyze the algorithm in the cases of noiseless and noisy data. The main analytic result of this paper shows that the coefficients of the identified feedback and feedforward transfer functions are arbitrarily close to the true coefficients if the data noise is sufficiently small and the candidate pool is sufficiently dense. This subsystem identification approach has application to modeling the control behavior of humans interacting with and receiving feedback from a dynamic system. We apply the algorithm to data from a human-in-the-loop experiment to model a human’s control behavior.
Keywords: Subsystem identification; Human-in-the-loop; Human motor control

Thomas Berger, Paul Van Dooren,
Computing the regularization of a linear differential–algebraic system,
Systems & Control Letters,
Volume 86,
2015,
Pages 48-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115001930)
Abstract: We study the regularization problem for linear differential–algebraic systems. As an improvement of former results we show that any system can be regularized by a combination of state-space and input-space transformations, behavioral equivalence transformations and a reorganization of variables. The additional state feedback which is needed in earlier publications is shown to be superfluous. We provide an algorithmic procedure for the construction of the regularization and discuss computational aspects.
Keywords: Differential–algebraic systems; Descriptor systems; Regularization; Behavioral approach

R. Rabah, G.M. Sklyar,
Exact observability and controllability for linear neutral type systems,
Systems & Control Letters,
Volume 89,
2016,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.12.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115002510)
Abstract: The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllability problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.
Keywords: Observability; Controllability; Duality; Neutral type systems

Kooktae Lee, Raktim Bhattacharya,
Stability analysis of large-scale distributed networked control systems with random communication delays: A switched system approach,
Systems & Control Letters,
Volume 85,
2015,
Pages 77-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115001784)
Abstract: In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays. The stability analysis is performed in the switched system framework, particularly as the Markov jump linear system. There have been considerable research on stability analysis of the Markov jump systems. However, these methods are not applicable to large-scale systems because large numbers of subsystems result in extremely large number of switching modes. To circumvent this scalability issue, we propose a new reduced mode model for stability analysis, which is computationally scalable. We also consider the case in which the transition probabilities for the Markov jump process contain uncertainties. We provide a new method that estimates bounds for uncertain Markov transition probability matrix to guarantee the system stability. Numerical example verifies the computational efficiency of the proposed methods.
Keywords: Large-scale distributed networked control system; Markov jump linear system; Switched system; Random communication delays

P. Rapisarda, A.C. Antoulas,
A bilinear differential forms approach to parametric structured state-space modelling,
Systems & Control Letters,
Volume 92,
2016,
Pages 14-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.02.014.
(http://www.sciencedirect.com/science/article/pii/S0167691116000438)
Abstract: We use one-variable Loewner techniques to compute polynomial-parametric models for MIMO systems from vector-exponential data gathered at various points in the parameter space. Instrumental in our approach are the connections between vector-exponential modelling via bilinear differential forms and the Loewner framework.
Keywords: Bilinear differential forms; Loewner approach; Parametric modelling

Shuzhen Yang,
The maximum principle for stochastic differential systems with general cost functional,
Systems & Control Letters,
Volume 90,
2016,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2016.01.001.
(http://www.sciencedirect.com/science/article/pii/S0167691116000037)
Abstract: In this paper, under the framework of Fréchet derivatives, we study a stochastic optimal control problem driven by a stochastic differential equation with general cost functional. By constructing a series of first-order and second-order adjoint equations, we establish the stochastic maximum principle and get the related Hamilton systems.
Keywords: Stochastic differential equations; Stochastic maximum principle; Hamilton systems

Ashish Cherukuri, Enrique Mallada, Jorge Cortés,
Asymptotic convergence of constrained primal–dual dynamics,
Systems & Control Letters,
Volume 87,
2016,
Pages 10-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.10.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115002078)
Abstract: This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer.
Keywords: Primal–dual dynamics; Constrained optimization; Saddle points; Discontinuous dynamics; Caratheodory solutions

Seyed Mehran Dibaji, Hideaki Ishii,
Consensus of second-order multi-agent systems in the presence of locally bounded faults,
Systems & Control Letters,
Volume 79,
2015,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115000419)
Abstract: We propose an algorithm for consensus of second-order sampled-data multi-agent systems in the presence of misbehaving agents. Each normal agent updates its states following a predetermined control law based on local information while some malicious agents make updates arbitrarily. The normal agents do not know the global topology of the network, but have prior knowledge on the maximum number of malicious agents in their neighborhood. Under the assumption that the network has sufficient connectivity in terms of robustness, we develop a resilient algorithm where each agent ignores the neighbors which have large and small position values to avoid being influenced by malicious agents.
Keywords: Multi-agent systems; Cyber-security; Consensus

Frédéric Mazenc, Emilia Fridman, Walid Djema,
Estimation of solutions of observable nonlinear systems with disturbances,
Systems & Control Letters,
Volume 79,
2015,
Pages 47-58,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.004.
(http://www.sciencedirect.com/science/article/pii/S016769111500064X)
Abstract: A family of continuous-time observable nonlinear systems with input and output is considered. A new technique of estimation of the state variables is proposed. It relies on the use of past values of the output, as done to construct some observers which converge in finite time, and on a recent technical result pertaining to the theory of the monotone systems. It applies to systems with additive disturbances and disturbances in the output. The nonlinear terms are not supposed to be globally Lipschitz, but it is requested that they depend only on the input and output variables.
Keywords: State estimation; Delay; Finite time observer; Robustness

Chetan D. Pahlajani, Jianxin Sun, Ioannis Poulakakis, Herbert G. Tanner,
Performance bounds for mismatched decision schemes with Poisson process observations,
Systems & Control Letters,
Volume 75,
2015,
Pages 69-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114002503)
Abstract: This paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time-inhomogeneous Poisson processes, when some parameters characterizing the observation process are not known exactly. Key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true, but intractable, error probabilities. The proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters. Using these tools, it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making. The results find direct application to problems of detecting illicit nuclear materials in transit.
Keywords: Decision making; Poisson process; Model mismatch; Nuclear detection

Christian Commault, Jean-Michel Dion,
The single-input Minimal Controllability Problem for structured systems,
Systems & Control Letters,
Volume 80,
2015,
Pages 50-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115000778)
Abstract: This paper considers the Minimal Controllability Problem (MCP), i.e. the problem of controlling a linear system with an input vector having as few non-zero entries as possible. We focus on structured systems which represent an interesting class of parameter dependent linear systems and look for structural controllability properties based on the sparsity pattern of the input vector. We show first that the MCP is solvable when a rank condition is satisfied and show that generically one non-zero entry in the input vector is sufficient to achieve controllability when there is no specific system structure. According to the fixed zero/non-zero pattern of the state matrix entries, we give an explicit characterization of the minimum number and the possible location of non-zero entries in the input vector to ensure generic controllability. The analysis based on graph tools provides with a simple polynomial MCP solution and highlights the structural mechanisms that make it useful to act on some variables to ensure controllability.
Keywords: Controllability; Structured system theory

Peng Yi, Yiguang Hong, Feng Liu,
Distributed gradient algorithm for constrained optimization with application to load sharing in power systems,
Systems & Control Letters,
Volume 83,
2015,
Pages 45-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115001346)
Abstract: In this paper, a distributed constrained optimization problem is discussed to achieve the optimal point of the sum of agents’ local objective functions while satisfying local constraints. Here neither the local objective function nor local constraint functions of each agent can be shared with other agents. To solve the problem, a novel distributed continuous-time algorithm is proposed by using the KKT condition combined with the Lagrangian multiplier method, and the convergence is proved with the help of Lyapunov functions and an invariance principle for hybrid systems. Furthermore, this distributed algorithm is applied to optimal load sharing control problem in power systems. Both theoretical and numerical results show that the optimal load sharing can be achieved within both generation and delivering constraints in a distributed way.
Keywords: Distributed optimization; Constrained optimization; Gradient flow; Multi-agent system; Load sharing control

A. Abdessameud, I.G. Polushin, A. Tayebi,
Motion coordination of thrust-propelled underactuated vehicles with intermittent and delayed communications,
Systems & Control Letters,
Volume 79,
2015,
Pages 15-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115000420)
Abstract: This paper addresses the coordinated control problem of under-actuated thrust-propelled vehicles with intermittent communication in the presence of varying communication delays. We propose a distributed control algorithm that achieves a prescribed formation for a team of vehicles that interact according to a directed graph containing a spanning tree. Each vehicle in the team is allowed to have access to its neighbors’ information only at an irregular sequence of time instants in the presence of possibly unbounded irregular communication delays and packet dropout. We show that our objective is reached under some easily verified conditions provided that the communication blackout intervals between each pair of neighbors are bounded. Simulations are provided to illustrate the effectiveness of the proposed control algorithm.
Keywords: Motion coordination; Cooperative control; Thrust-propelled vehicles; Intermittent communication; Communication delays; Under-actuated systems

Seddik M. Djouadi,
On robustness in the gap metric and coprime factor uncertainty for LTV systems,
Systems & Control Letters,
Volume 80,
2015,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115000663)
Abstract: In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller.
Keywords: Robust stabilization; Gap metric; Coprime factorization; Time-varying

Gökhan Şahan, Vasfi Eldem,
Well posedness conditions for Bimodal Piecewise Affine Systems,
Systems & Control Letters,
Volume 83,
2015,
Pages 9-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115001231)
Abstract: This paper considers well-posedness (the existence and uniqueness of the solutions) of Bimodal Piecewise Affine Systems in Rn. It is assumed that both modes are observable, but only one of the modes is in observable canonical form. This allows the vector field to be discontinuous when the trajectories change mode. Necessary and sufficient conditions for well-posedness are given as a set of algebraic conditions and sign inequalities. It is shown that these conditions induce a joint structure for the system matrices of the two modes. This structure can be used for the classification of well-posed bimodal piecewise affine systems. Furthermore, it is also shown that, under certain conditions, well-posed Bimodal Piecewise Affine Systems in Rn may have one or two equilibrium points or no equilibrium points.
Keywords: Switched systems; Bimodal systems; Well posedness; Existence and uniqueness; Carathéodory solution; Nonsmooth systems

Guosong Yang, Daniel Liberzon,
A Lyapunov-based small-gain theorem for interconnected switched systems,
Systems & Control Letters,
Volume 78,
2015,
Pages 47-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115000262)
Abstract: Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input-to-state stable (non-ISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic stability (GAS) of the interconnected system. For each switched system, with the constraints on the switching signal being modeled by an auxiliary timer, a correspondent hybrid system is defined to enable the construction of a hybrid ISS Lyapunov function. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected system is globally asymptotically stable.
Keywords: Interconnected systems; Small-gain theorems; Switched systems; Lyapunov methods; Hybrid systems

L.Z. Guo, Y.Z. Guo, S.A. Billings, D. Coca,
Approximate observability of infinite dimensional bilinear systems using a Volterra series expansion,
Systems & Control Letters,
Volume 75,
2015,
Pages 20-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114002357)
Abstract: In this paper, the approximate observability of a class of infinite dimensional bilinear systems is investigated. The observability conditions are discussed based on a Volterra series representation of this class of systems. A testable observability criterion is derived for the case where the infinitesimal generator is self-adjoint or Riesz-spectral operator. The theoretical results are illustrated by examples.
Keywords: Bilinear systems; Volterra series; Observability; Nonlinear systems


Editorial Board,
Systems & Control Letters,
Volume 84,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00159-0.
(http://www.sciencedirect.com/science/article/pii/S0167691115001590)

Lirong Huang, Håkan Hjalmarsson, Heinz Koeppl,
Almost sure stability and stabilization of discrete-time stochastic systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 26-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115001073)
Abstract: As is well known, noise may play a stabilizing or destabilizing role in continuous-time systems. But, for analysis and design of discrete-time systems, noise is treated as disturbance in the literature. This paper studies almost sure stability of general n-dimensional nonlinear time-varying discrete-time stochastic systems and presents a criterion based on a numerical result derived from Higham (2001), which exploits the stabilizing role of noise in discrete-time systems. As an application of the established results, this paper proposes a novel controller design method for almost sure stabilization of linear discrete-time stochastic systems. The effectiveness of the proposed design method is verified with an example (an aircraft model subject to state-dependent noise), to which the existing results do not apply.
Keywords: Almost sure stability; Stochastic difference equations; Discrete-time systems; State-feedback stabilization; Gaussian distribution

Liqing Lu, Shengjia Li, Goong Chen, Pengfei Yao,
Control and stabilization for the wave equation with variable coefficients in domains with moving boundary,
Systems & Control Letters,
Volume 80,
2015,
Pages 30-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.003.
(http://www.sciencedirect.com/science/article/pii/S016769111500081X)
Abstract: The study of stabilization and control for PDEs with variable coefficients involves higher level of complexity than the corresponding case of constant coefficients. Further compounding the complexity are the concern and effects of dynamic boundary motion. The problem in its general form is extremely challenging to treat, but under certain specific physical and geometric conditions, such as the time-likeness of the boundary and a limited speed of domain expansion, energy decay estimates can be established and the exact controllability can also be obtained by control-theoretic and Riemannian-geometric methods. Our approach here is based on the Bochner technique of differential geometry in terms of Riemannian metric and geometric multipliers, by generalizing an energy identity method used earlier in Bardos and Chen (1981). Concrete examples are also given to illustrate the geometric conditions and the theorems.
Keywords: Wave equation with variable coefficients; Moving boundary; Riemannian metric; Distance function of a metric


Editorial Board,
Systems & Control Letters,
Volume 79,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00070-5.
(http://www.sciencedirect.com/science/article/pii/S0167691115000705)


Editorial Board,
Systems & Control Letters,
Volume 80,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00094-8.
(http://www.sciencedirect.com/science/article/pii/S0167691115000948)

Christoforos Keroglou, Christoforos N. Hadjicostis,
Detectability in stochastic discrete event systems,
Systems & Control Letters,
Volume 84,
2015,
Pages 21-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115001516)
Abstract: A discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols, i.e., detectability captures the ability of an observer to eventually perfectly estimate the system state. In this paper we analyze detectability in stochastic discrete event systems (SDES) that can be modeled as probabilistic finite automata. More specifically, we define the notion of A-detectability, which characterizes our ability to estimate the current state of a given SDES with increasing certainty as we observe more output symbols. The notion of A-detectability is differentiated from previous notions for detectability in SDES because it takes into account the probability of problematic observation sequences (that do not allow us to perfectly deduce the system state), whereas previous notions for detectability in SDES considered each observation sequence that can be generated by the underlying system. We discuss observer-based techniques that can be used to verify A-detectability, and provide associated necessary and sufficient conditions. We also prove that A-detectability is a PSPACE-hard problem.
Keywords: Stochastic discrete event systems; Detectability; Stochastic detectability

Vladimir Gaitsgory, Lars Grüne, Neil Thatcher,
Stabilization with discounted optimal control,
Systems & Control Letters,
Volume 82,
2015,
Pages 91-98,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.010.
(http://www.sciencedirect.com/science/article/pii/S016769111500122X)
Abstract: We provide a condition under which infinite horizon discounted optimal control problems can be used in order to obtain stabilizing controls for nonlinear systems. The paper gives a mathematical analysis of the problem as well as an illustration by a numerical example.
Keywords: Stabilization; Discounted optimal control; Lyapunov function

Driss Boutat, Jean-Pierre Barbot, Mohamed Darouach,
On the inversion of a class of nonlinear systems,
Systems & Control Letters,
Volume 83,
2015,
Pages 38-44,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115001358)
Abstract: This paper deals with the inversion problem of affine square multi-input multi-output (MIMO) nonlinear systems. It presents a new algorithm unifying the construction of the inverse of a dynamical system with a regular or a singular characteristic matrix. This algorithm is based on the determination of a projector on the fibre bundle of the state space and incorporates a regularization of the singular case. It has the advantage of avoiding the input derivatives. Numerical examples are given to illustrate the proposed approach.
Keywords: Left invertibility; Inverse dynamics; Differential geometry

Seyed Mehdi Mirhosseini-Alizamini, Sohrab Effati, Aghileh Heydari,
An iterative method for suboptimal control of linear time-delayed systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 40-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115001115)
Abstract: This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.
Keywords: Time-delay systems; Pontryagin’s maximum principle; Variational iteration method; He’s polynomials; Suboptimal control

Guojie Zheng, Bao-Zhu Guo, M. Montaz Ali,
Continuous dependence of optimal control to controlled domain of actuator for heat equation,
Systems & Control Letters,
Volume 79,
2015,
Pages 30-38,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115000432)
Abstract: In this paper, we consider continuous dependence of the optimal control with respect to the actuator domain which is varying as open subset in the spatial domain for a multi-dimensional heat equation. Both time optimal control and norm optimal control problems are considered. The reason behind combining these two problems together is that these two problems are actually equivalent: The energy to be used to drive the system to target set in minimal time interval is actually the minimal energy of driving the system to target set in this minimal time interval, and visa versa. It is shown that both optimal control and optimal cost are continuous with respect to open controlled actuator domain under the Lebesgue measure.
Keywords: Heat equation; Time optimal control; Norm optimal control; Controlled domain; Continuous property

T. Ahmed-Ali, F. Giri, M. Krstic, F. Lamnabhi-Lagarrigue,
Observer design for a class of nonlinear ODE–PDE cascade systems,
Systems & Control Letters,
Volume 83,
2015,
Pages 19-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115001243)
Abstract: The problem of state-observation is addressed for nonlinear systems that can be modeled by an ODE–PDE series association. The ODE subsystem assumes a triangular structure while the PDE element is of heat diffusion type. The aim is to accurately estimate online the state vector of the ODE subsystem and the distributed state of the PDE element. One major difficulty is that the state observation must only rely on the global system output i.e. the PDE state at the terminal boundary. In particular, the connection point between the ODE and the PDE blocks is not accessible to measurements. The observation problem is dealt with by designing a high-gain type observer. Sufficient conditions involving the PDE domain length are formally established that ensure the observer exponential convergence.
Keywords: Observer design; Nonlinear systems; Distributed parameter systems

Dan Ma, Jun Zhao,
Stabilization of networked switched linear systems: An asynchronous switching delay system approach,
Systems & Control Letters,
Volume 77,
2015,
Pages 46-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115000031)
Abstract: In this paper, we investigate the network-dependent hybrid controller design for a class of networked switched linear systems. Networks with limited bandwidth cause the asynchronous motions between switched subsystems and the candidate controllers in both the state measurement and the switching signal. We rewrite the original networked switched systems by sampled asynchronous switched systems with time-varying delays. Using the asynchronous switched delay system method, we give the co-design conditions on both the switching signal and the controllers which depend on the sampling time, the upper bound of network-induced delays, the bound of the asynchronous switching time ratio and the asynchronous occurring frequency, under which the networked switched system is exponentially stable.
Keywords: Asynchronous switching stabilization; Network-induced delays; Switched linear systems

Thi-Minh-Dung Tran, Alain Y. Kibangou,
Distributed estimation of Laplacian eigenvalues via constrained consensus optimization problems,
Systems & Control Letters,
Volume 80,
2015,
Pages 56-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115000791)
Abstract: From the recent literature, we know that some consecutive measurements of the consensus protocol can be used to compute the exact average of the initial condition. In this paper, we show that these measurements can also be used for estimating the Laplacian eigenvalues of the graph representing the network. As recently shown in the literature, by solving the factorization of the averaging matrix, the Laplacian eigenvalues can be inferred. Herein, the problem is posed as a constrained consensus problem formulated two-fold. The first formulation (direct approach) yields a non-convex optimization problem solved in a distributed way by means of the method of Lagrange multipliers. The second formulation (indirect approach) is obtained after an adequate re-parameterization. The problem is then convex and is solved by using the distributed subgradient algorithm and the alternating direction method of multipliers (ADMM). The proposed algorithms allow estimating the actual Laplacian eigenvalues with high accuracy.
Keywords: Graph Laplacian eigenvalues; Matrix factorization; Distributed optimization; Distributed subgradient algorithms; Alternating direction method of multipliers (ADMM)

Liu Liu, Yufeng Lu,
Transitivity in simultaneous stabilization for a family of time-varying systems,
Systems & Control Letters,
Volume 78,
2015,
Pages 55-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115000274)
Abstract: This paper develops necessary and sufficient conditions for the so-called transitivity and strong transitivity (precise definitions later) for a family of discrete time-varying linear systems, which when satisfied lead to characterizations for simultaneous stabilizability and simultaneously stabilizing feedback controllers. Some criteria for the strong transitivity are established in terms of single coprime factorizations of only one plant and one controller, the resulting characterization involves coprime factorizations of fewer systems compared to previous work.
Keywords: Simultaneous stabilization; Transitivity; Nest algebra; Coprime factorization; Time-varying system

Bin Zhou,
Input delay compensation of linear systems with both state and input delays by adding integrators,
Systems & Control Letters,
Volume 82,
2015,
Pages 51-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115001085)
Abstract: This paper studies stabilization of linear systems with both state and input delays. A dynamic input-delay compensator obtained by adding integrators is established to compensate the input delays that can be arbitrarily large. With the input delay compensator, the original stabilization problem reduces to the problem of stabilizing an augmented linear time-delay system without input delay. Three methods are also proposed to design stabilizing controllers for the augmented linear time-delay system. The first method is based on linear matrix inequalities (LMIs) and the second method is based on model reduction. The third method is based on pole placement and is built for the particular case that the original time-delay system has only a pure delayed state vector on its right hand side. For this method, the optimal gain such that the decay rate of the closed-loop system is maximized is also proposed. The effectiveness of the proposed approaches is illustrated by three linear time-delay systems that are open-loop unstable.
Keywords: State and input delays; Adding integrators; Input delay compensation; Model reduction; Pole placement

Deepak Patil, Ameer Mulla, Debraj Chakraborty, Harish Pillai,
Computation of feedback control for time optimal state transfer using Groebner basis,
Systems & Control Letters,
Volume 79,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115000390)
Abstract: Computation of time optimal feedback control law for a controllable linear time invariant system with bounded inputs is considered. Unlike a recent paper by the authors, the target final state is not limited to the origin of state-space, but is allowed to be in the set of constrained controllable states. Switching surfaces are formulated as semi-algebraic sets using Groebner basis based elimination theory. Using these semi-algebraic sets, a nested switching logic is synthesized to generate the time optimal feedback control. However, the optimal control law enforces an unavoidable limit cycle in the time-optimal trajectory for most non-origin target points. The time-period of this limit-cycle is dependent on the target position. This dependence is algebraically characterized and a method to compute the time-period of the limit-cycle is provided. As a natural extension, the set of constrained controllable states is also computed.
Keywords: Time optimal control; Feedback; Groebner basis; Limit cycle

Corentin Briat,
Stability analysis and control of a class of LPV systems with piecewise constant parameters,
Systems & Control Letters,
Volume 82,
2015,
Pages 10-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115000912)
Abstract: Stability criteria characterizing the asymptotic stability of a class of LPV systems with piecewise constant parameters under constant and minimum dwell-time are derived. It is shown that, for such systems, the conditions for the stability under minimum dwell-time can be seen as a unifying stability concept lying in between quadratic and robust stability, thereby including them as extremal cases. The results are then extended to address the stabilization problem using a particular class of time-dependent gain-scheduled state-feedback controllers. Several examples are given for illustration.
Keywords: LPV systems; Gain-scheduling; Dwell-time

Miloje S. Radenković, Mark Gołkowski,
Distributed self-tuning consensus and synchronization,
Systems & Control Letters,
Volume 76,
2015,
Pages 66-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114002722)
Abstract: The problem of self-tuning of coupling parameters in multi-agent systems is considered. Agent dynamics are described by a discrete-time double integrator with unknown input gain. Each agent locally tunes the strength of interaction with neighboring agents by using a normalized gradient algorithm (NGA). The tuning algorithm minimizes the square of the error between an individual agent’s state (velocity) and the one step delayed average of its own state and the states of its neighbors. Assuming that the network graph is strongly connected, it is proved that the sequence of coupling parameters is convergent and all velocities converge toward the same constant value.
Keywords: Multi-agent systems; Distributed consensus; Synchronization; Cooperative phenomena

Naohisa Otsuka,
Disturbance decoupling via measurement feedback for switched linear systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 99-107,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115001206)
Abstract: The disturbance decoupling problems via measurement feedback for switched linear systems are studied in the framework of the so-called geometric approach. At first, the robust (Ci∈I,Ai∈I,Bi∈I)-pair which incorporates both the concepts of robust controlled (Ai∈I,Bi∈I)-invariant and its dual robust conditioned (Ci∈I,Ai∈I)-invariant subspaces for a family of linear systems is investigated. Next, disturbance decoupling problems via dynamic and/or static measurement feedback under arbitrary switching for switched linear systems are formulated, and necessary and sufficient conditions for the problems to be solvable are presented. After that the stabilization for disturbance decoupled systems under arbitrary switching is also discussed. Finally, an illustrative numerical example is given.
Keywords: A geometric approach; A family of linear systems; Disturbance decoupling; Switched linear systems; Arbitrary switching; Measurement feedback

Ferdinand Küsters, Markus G.-M. Ruppert, Stephan Trenn,
Controllability of switched differential–algebraic equations,
Systems & Control Letters,
Volume 78,
2015,
Pages 32-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115000237)
Abstract: We study controllability of switched differential–algebraic equations. We are able to establish a controllability characterization where we assume that the switching signal is known. The characterization takes into account possible jumps induced by the switches. It turns out that controllability not only depends on the actual switching sequence but also on the duration between the switching times.
Keywords: Switched systems; Differential–algebraic systems; Descriptor systems; Controllability

Ya Zhang, Yu-Ping Tian,
Consensus tracking in sensor networks with periodic sensing and switching connected topologies,
Systems & Control Letters,
Volume 84,
2015,
Pages 44-51,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115000882)
Abstract: This paper studies the consensus tracking of general linear dynamical target in periodically sensing networks with switching and connected sensing topologies. Allowable upper bounds of sensing period are investigated for both time-invariant sensing and time-varying sensing networks. For tracking system with constant sensing period, discretization approach is applied and the tracking problem under switching connected topologies is converted to the robust stability problem of a discrete-time uncertain system. Then an allowable upper bound of sensing period is given by solving optimal H∞ control problem, and an explicit bound, which is composed of the eigenvalues of target’s dynamic matrix and topology matrix, is further provided. For tracking system with time-varying sensing period, input-delay approach is applied and a bound is given by using Lyapunov–Krasovskii functional analysis and solving the feasibility of three LMIs. Numerical examples are given to illustrate the results.
Keywords: Consensus tracking; Multi-agent system; Periodic sensing; Switching topologies

R. Zanasi, F. Grossi, L. Biagiotti,
Qualitative graphical representation of Nyquist plots,
Systems & Control Letters,
Volume 83,
2015,
Pages 53-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115001334)
Abstract: In this paper, the procedure for manually drawing the Nyquist plot of a generic transfer function is revised and, in particular, two novel parameters (Δτ, Δp), which allow to simplify this process, are presented. Thanks to these parameters, the analysis of the frequency response at low and high frequencies is considerably enhanced, with a very little effort. These parameters allow to predict initial and final directions of the polar curve in the vicinity of initial and final points and consequently the sectors of the complex plane where the plot starts/ends. In many cases it is possible to obtain a qualitative Nyquist plot, able to correctly predict the stability properties of the closed-loop system, by simply joining the initial and final tracts found with the proposed procedure. Moreover, the analysis based on these parameters can aid to correctly interpret the plots obtained with computer programs which often, in particular when poles at the origin are present, hide the behavior of the frequency response in the area close to the origin of the complex plane.
Keywords: Nyquist plot; Frequency response; Stability analysis

Sergey Dashkovskiy, Lars Naujok,
Quasi-ISS/ISDS observers for interconnected systems and applications,
Systems & Control Letters,
Volume 77,
2015,
Pages 11-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114002692)
Abstract: This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading effect, with reduced-order observers to obtain quantitative information about the state estimate error. Considering interconnections quasi-ISS/ISDS reduced-order observers for each subsystem are derived, where suitable error Lyapunov functions for the subsystems are used. Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used. As an application, we prove that quantized output feedback stabilization for each subsystem and the overall system is achievable, when the systems possess a quasi-ISS/ISDS reduced-order observer and a state feedback law that yields ISS/ISDS for each subsystem and therefor the overall system with respect to measurement errors. Using dynamic quantizers it is shown that under the mentioned conditions asymptotic stability can be achieved for each subsystem and for the whole system.
Keywords: Reduced-order observers; Interconnected systems; Input-to-state dynamical stability; Small-gain condition; Lyapunov functions; Quantized output feedback


Editorial Board,
Systems & Control Letters,
Volume 76,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00012-2.
(http://www.sciencedirect.com/science/article/pii/S0167691115000122)

Mehdi Hosseinzadeh, Mohammad Javad Yazdanpanah,
Performance enhanced model reference adaptive control through switching non-quadratic Lyapunov functions,
Systems & Control Letters,
Volume 76,
2015,
Pages 47-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114002576)
Abstract: Based on the model reference adaptive scheme, a robust adaptive tracking controller for systems with arbitrary relative degree and known high-frequency gain is proposed. To cope with the difficulty raised by swapping lemma for systems with relative degree beyond one, a new variable related to the tracking error is defined. It is also indicated that if the new defined variable converges to zero asymptotically with time, so does the tracking error. In the line of achieving adaptation laws, a non-quadratic Lyapunov function with one degree of freedom called α is considered, where α=1 corresponds to a quadratic Lyapunov function. Effects of choosing different values for α on the response of the system is studied analytically. It is shown that using a multi-criterion α may lead to a faster response compared to that of α=1. For enhancing the tracking performance, a switching scheme is designed in a constructive manner. Using projection technique to prevent parameter drift, it is shown analytically that the proposed scheme is robust against bounded disturbances. It is also indicated that for systems with relative degree one, knowing the high-frequency gain can be relaxed. Two examples are presented to show the effectiveness of the proposed approach: (1) a numerical example as a system with relative degree one, (2) the speed control of DC motor as a system with a relative degree larger than one.
Keywords: Adaptive tracking; Model Reference Adaptive Control (MRAC); Non-quadratic Lyapunov function; Robust performance

Zhishan Liang, Qingrong Liu,
Design of stabilizing controllers of upper triangular nonlinear time-delay systems,
Systems & Control Letters,
Volume 75,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114002333)
Abstract: In this paper, it is considered the state feedback controller design for a class of upper triangular nonlinear systems with simultaneous input and state delays. By using the state transformation of nonlinear systems, the problem of designing controller can be converted into that of designing a dynamic parameter, which is dynamically regulated by a dynamic equation. Then, by appraising the nonlinear terms of the given systems, a dynamic equation can be delicately constructed. At last, with the help of Lyapunov stability theorem, it is provided the stability analysis for the closed-loop system consisting of the designed controller and the given systems. Both discrete delays and continuous delays with integral form are considered here. Different from many existing control designs for upper triangular nonlinear systems, neither forwarding recursive nor saturation computation is utilized here, and thus our design procedure is simpler. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Keywords: Upper triangular systems; Time-delay systems; Lyapunov method; Dynamic gain controllers

T.M.P. Gommans, W.P.M.H. Heemels,
Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach,
Systems & Control Letters,
Volume 79,
2015,
Pages 59-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115000481)
Abstract: In systems with resource constraints, such as actuation limitations or limited communication bandwidth, it is desired to obtain control signals that are either sparse or sporadically changing in time to reduce resource utilization. In this paper, we propose a resource-aware self-triggered MPC strategy for discrete-time nonlinear systems subject to state and input constraints that has three important features: Firstly, significant reductions in resource utilization can be realized without modifying the cost function by input regularization or explicitly penalizing resource usage. Secondly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels (in terms of the original cost function) are guaranteed by design next to asymptotic stability and constraint satisfaction. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of numerical examples, we show the effectiveness of this novel strategy.
Keywords: Self-triggered control; Model predictive control; Sparse control; Networked control systems

Jinghui Suo, Jitao Sun,
Convergence domain for time-varying switched systems,
Systems & Control Letters,
Volume 78,
2015,
Pages 19-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115000080)
Abstract: In this paper, we investigate the convergence domain for time-varying switched systems. We construct multiple Lyapunov functions and each Lyapunov function is decreasing outside a ball whose radius is time-varying. We give a relatively accurate convergence domain for a general time-varying switched system. Finally, a numerical example, a mass–spring–damper system, is provided to show the effectiveness of the theoretical results.
Keywords: Switched systems; Convergence domain; Multiple Lyapunov functions

Yu Zhao, Zhisheng Duan, Guanghui Wen, Guanrong Chen,
Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration,
Systems & Control Letters,
Volume 81,
2015,
Pages 8-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.002.
(http://www.sciencedirect.com/science/article/pii/S0167691115000808)
Abstract: This paper addresses the distributed finite-time tracking problem for a group of mobile agents modeled by double-integrator dynamics under a leader with bounded unknown acceleration. First, a distributed finite-time tracking protocol is designed based on both the relative position and the relative velocity measurements. This protocol can drive the states of the followers to track the leader in finite time under the constraint that the leader’s acceleration is bounded but unknown to the followers. Then, a novel position-based tracking protocol is designed and analyzed for solving the distributed finite-time tracking problem when both velocity and acceleration measurements are not available for the followers. It is theoretically proved that the followers can move to be with the leader in finite time if the network topology is undirected among the followers but has a directed path from the leader to each follower. In particular, the position-based protocol does not require the relative input information between the agents. Finally, the effectiveness of the algorithms is illustrated by numerical simulations.
Keywords: Distributed control; Finite-time tracking; Multi-agent system; Observer-based protocol; Relative measurement

Amir Ajorlou, Mohammad Mehdi Asadi, Amir G. Aghdam, Stephane Blouin,
Distributed consensus control of unicycle agents in the presence of external disturbances,
Systems & Control Letters,
Volume 82,
2015,
Pages 86-90,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115000924)
Abstract: In this paper, a distributed consensus control strategy is presented for a team of unicycle agents subject to external disturbances. Bounded disturbances with unknown dynamics on both translational and angular velocities are applied to the system. The key idea is to design the control inputs of each agent in such a way that, after a finite time, agents move with an acute angle with respect to a reference vector typically used for the consensus control of disturbance-free single-integrator agents. Convergence to consensus is then proved using Lyapunov theory. Simulation results confirm the efficacy of the proposed controller.
Keywords: Multi-agent systems; Distributed consensus control; External disturbance rejection; Unicycle agents

Tianrui Chen, Cong Wang, David J. Hill,
Small oscillation fault detection for a class of nonlinear systems with output measurements using deterministic learning,
Systems & Control Letters,
Volume 79,
2015,
Pages 39-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115000407)
Abstract: Early detection of small faults is an important issue in the literature of fault diagnosis. In this paper, for a class of nonlinear systems with output measurements, an approach for rapid detection of small oscillation faults is presented. Firstly, locally accurate approximations of unknown system dynamics and fault functions are achieved by combining a high gain observer and a deterministic learning (DL) theory. The obtained knowledge of system dynamics for both normal and fault modes is stored in constant RBF networks. Secondly, a bank of dynamical estimators are constructed for all the normal mode and oscillation faults. The knowledge obtained through DL is reused with a nonhigh-gain design. The occurrence of a fault can be detected if one of residual norms of a fault estimator becomes smaller than that of the normal estimator in a finite time. A rigorous analysis of the detectability properties of the proposed fault detection scheme is also given, which includes the fault detectability condition and the fault detection time. The attractions of the paper lie in that with output measurements, the knowledge of modeling uncertainty and nonlinear faults is obtained and then is utilized to enhance the sensitivity to small faults.
Keywords: Fault detection; Deterministic learning; Observer; Persistent excitation (PE) condition; Radial basis function neural networks

Lei Wang, Alberto Isidori, Hongye Su,
Output feedback stabilization of nonlinear MIMO systems having uncertain high-frequency gain matrix,
Systems & Control Letters,
Volume 83,
2015,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115001218)
Abstract: The purpose of this paper is to provide a method for (semi-global) asymptotic stabilization of a nonlinear minimum-phase MIMO system, under a mild hypothesis of the so-called “high-frequency gain” matrix. This result is based on a non-trivial extension, to the MIMO setting, of the approach based on the use of extended observers. As a byproduct, a dynamic output feedback control is obtained, that asymptotically stabilizes the equilibrium of the closed-loop system, in spite of uncertainties in the high-frequency gain matrix.
Keywords: MIMO nonlinear systems; Normal forms; Minimum-phase systems; Extended observers; Output feedback

M. Souza, J.C. Geromel, P. Colaneri, R.N. Shorten,
Discretisation of sparse linear systems: An optimisation approach,
Systems & Control Letters,
Volume 80,
2015,
Pages 42-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115000766)
Abstract: This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices. Numerical examples are included.
Keywords: Discretisation; Linear systems; LMI

Corentin Briat,
Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time,
Systems & Control Letters,
Volume 78,
2015,
Pages 63-72,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115000249)
Abstract: Alternative conditions for establishing dwell-time stability properties of linear switched systems are considered. Unlike the hybrid conditions derived in Geromel and Colaneri (2006), the considered ones are affine in the system matrices, allowing then for the consideration of uncertain switched systems with time-varying uncertainties. The low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state-feedback control laws. The resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped-functionals previously considered in the literature. The sums of squares conditions are also proven to (1) approximate arbitrarily well the conditions of Geromel and Colaneri (2006); and (2) be invariant with respect to time-scaling, emphasizing that the complexity of the approach does not depend on the size of the dwell-time. Several comparative examples illustrate the efficiency of the approach.
Keywords: Switched systems; Dwell-time; Stabilization; Robustness; Sum of squares

Islam Boussaada, Irinel-Constantin Morărescu, Silviu-Iulian Niculescu,
Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains,
Systems & Control Letters,
Volume 82,
2015,
Pages 1-9,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.002.
(http://www.sciencedirect.com/science/article/pii/S016769111500047X)
Abstract: The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.
Keywords: Time-delay; Stability; Delayed feedback; Nonhyperbolic dynamics; Center manifold; Normal forms; Local bifurcation analysis; Inverted pendulum

Alejandro D. Domínguez-García, Christoforos N. Hadjicostis,
Distributed resource coordination in networked systems described by digraphs,
Systems & Control Letters,
Volume 82,
2015,
Pages 33-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.012.
(http://www.sciencedirect.com/science/article/pii/S0167691115001103)
Abstract: We consider a multicomponent system in which each component can receive/transmit information from/to components in its immediate neighborhood. Communication links between components are not required to be bidirectional, so that the information exchange between components in the system is in general described by a directed graph (digraph). Each component can contribute a certain amount of some resource (of the same type for each component), and the objective is for the components to distributively compute their individual resource contribution so as to collectively provide a requested amount of the resource. A further constraint is that each component’s contribution is upper and lower bounded by locally known capacity constraints. In order to solve this resource coordination problem, we propose a distributed linear iterative algorithm in which each component maintains a set of values that are updated to be weighted linear combinations of its own previous value(s) and the values of the components it receives information from. Since the original choices of weights used by the components to perform the linear updates may not allow the components to solve the problem, the weights are allowed to adapt (also in a distributed fashion) as the algorithm progresses. Convergence of the proposed algorithm to a feasible solution is established analytically and demonstrated via examples.
Keywords: Coordination; Distributed iterative algorithms; Perron–Frobenius theorem; Stochastic matrices

Michael Gil’,
Stability of linear nonautonomous multivariable systems with differentiable matrices,
Systems & Control Letters,
Volume 81,
2015,
Pages 31-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115000651)
Abstract: We consider linear nonautonomous multivariable systems with differentiable matrices. Explicit stability conditions are derived. In the appropriate situations our results improve the traditional freezing method.
Keywords: Linear systems; Stability

György Lipták, Gábor Szederkényi, Katalin M. Hangos,
Computing zero deficiency realizations of kinetic systems,
Systems & Control Letters,
Volume 81,
2015,
Pages 24-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115000894)
Abstract: In the literature, there exist strong results on the qualitative dynamical properties of chemical reaction networks (also called kinetic systems) governed by the mass action law and having zero deficiency. However, it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations. In this paper, an optimization-based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics. Through establishing an equivalent condition for zero deficiency, the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem. Furthermore, it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming. Two examples are given for the illustration of the proposed methods.
Keywords: Nonnegative systems; Kinetic systems; Optimization; Chemical reaction networks; Dynamical equivalence

Eduardo Castañeda-Toledo, Vladimír Kučera, Javier Ruiz-León,
Realization of full column rank precompensators using stabilizing static state feedback,
Systems & Control Letters,
Volume 76,
2015,
Pages 42-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.012.
(http://www.sciencedirect.com/science/article/pii/S0167691114002564)
Abstract: In some control problems, it is convenient to use a precompensator to alter the transfer function of the system such that the transfer function of the compensated system has a specified property. Then, if possible, the action of the compensator on the system is realized by a static state feedback law applied to the system. When the compensator is square and non-singular, the state feedback is regular and the problem has already been solved. Non-square compensators, however, result in non-regular state feedback. In this paper, necessary and sufficient conditions are presented for the compensated system to be stabilizable by such a non-regular static state feedback law.
Keywords: Linear systems; State feedback; Feedback realizability; Model matching; Stabilization

Thomas Berger, Timo Reis,
Regularization of linear time-invariant differential–algebraic systems,
Systems & Control Letters,
Volume 78,
2015,
Pages 40-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.013.
(http://www.sciencedirect.com/science/article/pii/S0167691115000250)
Abstract: We derive equivalent criteria for the existence of a feedback ensuring that a given linear and time-invariant differential–algebraic control system is regular or autonomous, respectively. Algebraic and geometric criteria are stated in terms of the involved matrices and the augmented Wong sequences. For systems which are not regularizable by feedback, we show that an additional behavioral equivalence transformation and a reorganization of input and state variables leads to a regular system, the index of which is at most one. This procedure is known, however our approach allows for a detailed characterization of the resulting regular system.
Keywords: Differential–algebraic systems; Descriptor systems; Regularization; Behavioral approach; Feedback; Wong sequences

Ying Yang, Steven X. Ding, Linlin Li,
On observer-based fault detection for nonlinear systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 18-25,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115001061)
Abstract: This paper addresses analysis and integrated design of observer-based fault detection (FD) for nonlinear systems. To gain a deeper insight into the observer-based FD framework, definitions and existence conditions for nonlinear observer-based FD systems are studied first. Then, a scheme for an integrated design of observer-based FD systems for affine nonlinear systems is proposed. Our work is considerably inspired by the study on input–output stability and stabilization of nonlinear systems. Examples are given at the end of the paper to illustrate the theoretical results.
Keywords: Fault detection; Nonlinear observer-based residual generation; Input–output stability

Mohamed Mabrok, Abhijit G. Kallapur, Ian R. Petersen, Alexander Lanzon,
A generalized negative imaginary lemma and Riccati-based static state-feedback negative imaginary synthesis,
Systems & Control Letters,
Volume 77,
2015,
Pages 63-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115000092)
Abstract: In this paper, we present a generalized negative imaginary lemma based on a generalized negative imaginary system definition. Then, an algebraic Riccati equation method is given to determine if a system is negative imaginary. Also, a state feedback control procedure is presented that stabilizes an uncertain system and leads to the satisfaction of the negative imaginary property. The controller synthesis procedure is based on the proposed negative imaginary lemma. Using this procedure, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the results.
Keywords: Negative imaginary systems; Riccati equations; Uncertain systems

Daniel Axehill,
Controlling the level of sparsity in MPC,
Systems & Control Letters,
Volume 76,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114002680)
Abstract: In optimization algorithms used for on-line Model Predictive Control (MPC), linear systems of equations are often solved in each iteration. This is true both for Active Set methods as well as for Interior Point methods, and for linear MPC as well as for nonlinear MPC and hybrid MPC. The main computational effort is spent while solving these linear systems of equations, and hence, it is of greatest interest to solve them efficiently. Classically, the optimization problem has been formulated in either of two ways. One leading to a sparse linear system of equations involving relatively many variables to compute in each iteration and another one leading to a dense linear system of equations involving relatively few variables. In this work, it is shown that it is possible not only to consider these two distinct choices of formulations. Instead it is shown that it is possible to create an entire family of formulations with different levels of sparsity and number of variables, and that this extra degree of freedom can be exploited to obtain even better performance with the software and hardware at hand. This result also provides a better answer to a recurring question in MPC; should the sparse or dense formulation be used.
Keywords: Predictive control; Optimization; Riccati recursion; Sparsity

Jan Maximilian Montenbruck, Mathias Bürger, Frank Allgöwer,
Synchronization of diffusively coupled systems on compact Riemannian manifolds in the presence of drift,
Systems & Control Letters,
Volume 76,
2015,
Pages 19-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114002709)
Abstract: Recently, it has been shown that the synchronization manifold is an asymptotically stable invariant set of diffusively coupled systems on Riemannian manifolds. We regionally investigate the stability properties of the synchronization manifold when the systems are subject to drift. When the drift vector field is quad (i.e. satisfies a certain quadratic inequality) and the underlying Riemannian manifold is compact, we prove that a sufficiently large algebraic connectivity of the underlying graph is sufficient for the synchronization manifold to remain asymptotically stable. For drift vector fields which are quad or contracting, we explicitly characterize the rate at which the solution converges to the synchronization manifold. Our main result is that the synchronization manifold is asymptotically stable even for drift vector fields which are only locally Lipschitz continuous, as long as the algebraic connectivity of the underlying graph is sufficiently large.
Keywords: Synchronization; Drift; Lyapunov stability; Nonlinear systems

Yuhu Wu, Tielong Shen,
An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 108-114,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115000857)
Abstract: This paper investigates the finite horizon optimal control problem for the stochastic logical dynamical systems with finite states. After giving the equivalent descriptions of stochastic logical dynamical system in term of Markov process, the finite horizon optimization problem is presented in an algebraic form. Based on semi-tensor product of matrix and the increasing dimensional technique, a succinct algebraic expression of dynamic programming algorithm is derived to solve the optimal control problem. Examples, including an application on stochastic Kleene’s logical optimization problem, are presented to show the effectiveness of our main result.
Keywords: Logical control; Finite horizon optimal control; Stochastic logical dynamical systems

Moritz Schulze Darup, Martin Mönnigmann,
A stabilizing control scheme for linear systems on controlled invariant sets,
Systems & Control Letters,
Volume 79,
2015,
Pages 8-14,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115000456)
Abstract: We present a new stabilizing control scheme for linear discrete-time systems with input and state constraints. Essentially, we seek a controller that is able to steer all initial states within a controlled invariant set towards the origin without violating the constraints. The control law builds on a predictive control scheme. We show that a prediction horizon of n steps, where n denotes the dimension of the system, is sufficient to solve the described control task. The proposed controller is related to but different from established feedback laws associated with λ-contractive sets. In fact, the new control scheme successfully stabilizes systems, where classical λ-contractive control laws fail.
Keywords: Linear discrete-time systems; Input and state constraints; Asymptotic stability; Control laws


Editorial Board,
Systems & Control Letters,
Volume 82,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00127-9.
(http://www.sciencedirect.com/science/article/pii/S0167691115001279)

Nima Monshizadeh, Shuo Zhang, M. Kanat Camlibel,
Disturbance decoupling problem for multi-agent systems: A graph topological approach,
Systems & Control Letters,
Volume 76,
2015,
Pages 35-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114002552)
Abstract: This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a “topological translation” of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example.
Keywords: Disturbance decoupling; Multi-agent systems; Graph partitions; Almost equitable partitions

Tobias Breiten, Christopher Beattie, Serkan Gugercin,
Near-optimal frequency-weighted interpolatory model reduction,
Systems & Control Letters,
Volume 78,
2015,
Pages 8-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115000067)
Abstract: This paper develops an interpolatory framework for weighted-H2 model reduction of MIMO dynamical systems. A new representation of the weighted-H2 inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-H2 reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions given by Halevi is also shown. An examination of realizations for equivalent weighted-H2 systems leads then to an algorithm that remains tractable for large state-space dimension. Several numerical examples illustrate the effectiveness of this approach and its competitiveness with Frequency Weighted Balanced Truncation and an earlier interpolatory approach, the Weighted Iterative Rational Krylov Algorithm.
Keywords: Frequency-weighting; Interpolation; Controller reduction; H2 model reduction

Wenchao Huang, Jianping Zeng, Hongfei Sun,
Robust consensus for linear multi-agent systems with mixed uncertainties,
Systems & Control Letters,
Volume 76,
2015,
Pages 56-65,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114002710)
Abstract: This paper studies the robust consensus problem for a class of linear multi-agent systems (MASs) with polytopic uncertainties and external disturbances. The uncertainties appear in both the dynamics of each agent and the topology of the overall network. Based on Lyapunov stability theory, the robust consensus problem is converted to the robust H∞ stabilization of the error system. With the aid of the homogeneous parameter-dependent (HPD) Lyapunov functions and sum of squares (SOS) technique, the robust consensus problem is further formulated as an SOS programming. Sufficient conditions to achieve robust consensus with disturbance rejection capability are presented in terms of SOS constraints. As an extension, the robust consensus problem for discrete-time MASs is studied in a similar way. Numerical examples are provided to illustrate the effectiveness of the approach.
Keywords: Multi-agent system (MAS); Homogeneous parameter-dependent linear matrix inequality (HPD-LMI); Robust consensus; Directed graph

Fengzhong Li, Yungang Liu,
Global stabilization via time-varying output-feedback for stochastic nonlinear systems with unknown growth rate,
Systems & Control Letters,
Volume 77,
2015,
Pages 69-79,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115000109)
Abstract: This paper considers the global stabilization via time-varying output-feedback for a class of stochastic nonlinear systems. Different from the related existing literature, the systems possess serious uncertainties/unknowns which are reflected in the uncertain control coefficient and the unknown growth rate of the unmeasured states dependent growth. To deal with these serious uncertainties/unknowns, a time-varying framework, rather than an adaptive one, is proposed in this paper since the latter has not been successfully employed in the topic. Detailedly, due to the absence of precise information on the control coefficient, time-varying K-filters are introduced to construct the unmeasured system states. By a delicate time-scaling transformation, a time-scaled entire system is derived, and from which, the design scheme of a time-varying output-feedback controller is developed by backstepping method and time-varying technique. It is shown that all signals of the resulting closed-loop system converge to zero a.s., and furthermore, when serious time-variations exist as well, it suffices to find a fast enough time-varying gain for the control design scheme. A simulation example is given to show the effectiveness of the theoretical results.
Keywords: Stochastic nonlinear systems; Stabilization; Output-feedback; K-filters; Time-varying technique

Qingxin Meng, Yang Shen,
A revisit to stochastic near-optimal controls: The critical case,
Systems & Control Letters,
Volume 82,
2015,
Pages 79-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115000869)
Abstract: This paper revisits the stochastic near-optimal control problem considered in Zhou (1998), where the stochastic system is given by a controlled stochastic differential equation with the control variable taking values in a general control space and entering both the drift and diffusion coefficients. A necessary condition of near-optimality is derived using Ekeland’s variational principle, spike variation techniques, and some delicate estimates for the state and the adjoint processes. We improve the error bound of order from “almost” ε13 in Zhou (1998) to “exactly” ε13.
Keywords: Stochastic near-optimal control; Necessary condition; Maximum principle; Ekeland’s variational principle; Error bound

Ion Necoara,
Computational complexity certification for dual gradient method: Application to embedded MPC,
Systems & Control Letters,
Volume 81,
2015,
Pages 49-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.011.
(http://www.sciencedirect.com/science/article/pii/S0167691115000900)
Abstract: In this paper we analyze the computational complexity of the dual gradient method for solving linearly constrained convex problems. When it is difficult to project on the primal feasible set described by linear constraints, we use the Lagrangian relaxation to handle the complicated constraints and then, we apply the dual gradient algorithm for solving the corresponding dual. We give a unified convergence rate analysis for the dual gradient algorithm: we provide sublinear or linear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. Our analysis relies on the Lipschitz property of the dual function or an error bound property. Furthermore, the iteration complexity analysis is based on two types of approximate primal solutions: an average primal sequence or the last primal iterate sequence. We also discuss complexity certifications and implementation aspects of the dual gradient algorithm on constrained MPC problems for embedded linear systems.
Keywords: Dual gradient; Linear/sublinear convergence rate; Complexity certification; Embedded model predictive control

Dong Shen, Youqing Wang,
ILC for networked nonlinear systems with unknown control direction through random Lossy channel,
Systems & Control Letters,
Volume 77,
2015,
Pages 30-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.008.
(http://www.sciencedirect.com/science/article/pii/S016769111400276X)
Abstract: The iterative learning control is constructed for the discrete-time networked nonlinear systems with random measurement losses and unknown control direction, which have not been studied simultaneously in literature. Differing from the conventional Bernoulli random variable model, the random packet loss is modeled by an arbitrary stochastic sequence with bounded length requirement, which is a new model of realistic packet losses. A novel regulating approach based on truncations is introduced to make the proposed algorithm find the correct control direction adaptively, and then guarantee the almost sure convergence property. Therefore, this paper has three major innovations compared with reported studies, namely, the stochastic sequence model of packet loss, the novel control direction regulation method, and the almost sure convergence property of the proposed algorithm. An illustrative example shows the effectiveness of the proposed approach.
Keywords: Iterative learning control; Networked control system; Random packet losses; Stochastic approximation


Editorial Board,
Systems & Control Letters,
Volume 83,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00143-7.
(http://www.sciencedirect.com/science/article/pii/S0167691115001437)

Zhifei Zhang, Alain Sarlette, Zhihao Ling,
Integral control on Lie groups,
Systems & Control Letters,
Volume 80,
2015,
Pages 9-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.02.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115000468)
Abstract: In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of “integral action” for proportional(–derivative)-controlled systems whose configuration evolves on a nonlinear space, where configuration errors cannot be simply added up to compute a definite integral. We then prove that the proposed integral control allows to cancel the drift induced by a constant bias in both first order (velocity) and second order (torque) control inputs for fully actuated systems evolving on abstract Lie groups. We illustrate the approach by 3-dimensional motion control applications.
Keywords: PID control; Riemannian manifolds; Lie groups; Bias rejection

Francisco Javier Bejarano,
Detectability of linear systems over a principal ideal domain with unknown inputs,
Systems & Control Letters,
Volume 78,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115000079)
Abstract: Observability and detectability conditions are obtained for a sort of linear time invariant systems affected by unknown inputs. It is assumed that the system can be described using matrices whose elements are within a principal ideal domain (PID). It is shown that, under suitable hypothesis, the obtained conditions are necessary and sufficient. The analysis is carried out by making use of the Smith normal form of matrices over a PID. The obtained conditions are a generalization of known conditions for particular sorts of systems which are included in those considered here.
Keywords: Detectability; Systems over rings; Unknown input observability; Uncertain systems


Editorial Board,
Systems & Control Letters,
Volume 78,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00059-6.
(http://www.sciencedirect.com/science/article/pii/S0167691115000596)

T.S. Doan, A. Kalauch, M. Klose, S. Siegmund,
Stability of positive linear switched systems on ordered Banach spaces,
Systems & Control Letters,
Volume 75,
2015,
Pages 14-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114002266)
Abstract: We provide sufficient criteria for the stability of positive linear switched systems on ordered Banach spaces. The switched systems can be generated by finitely many bounded operators in infinite-dimensional spaces with a general class of order-inducing cones. In the discrete-time case, we assume an appropriate interior point of the cone, whereas in the continuous-time case an appropriate interior point of the dual cone is sufficient for stability. This is an extension of the concept of linear Lyapunov functions for positive systems to the setting of infinite-dimensional partially ordered spaces. We illustrate our results with examples.
Keywords: Linear positive switched systems; Ordered Banach space; Stability

Jing Zhu, Tian Qi, Jie Chen,
Small-gain stability conditions for linear systems with time-varying delays,
Systems & Control Letters,
Volume 81,
2015,
Pages 42-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115000870)
Abstract: In this paper we show that a variety of stability conditions, both existing and new, can be derived for linear systems subject to time-varying delays in a unified manner in the form of scaled small-gain conditions. From a robust control perspective, our development seeks to cast the stability problem as one of robust stability analysis, and the resulting stability conditions are also reminiscent of robust stability bounds typically found in robust control theory. The development is built on the well-known conventional robust stability analysis, requiring essentially no more than a straightforward application of the small gain theorem. The derived conditions have conceptual appeal, and they can be checked using standard robust control toolboxes.
Keywords: Delay systems; Time-varying delays; Small-gain conditions

Guang-Song Han, Zhi-Hong Guan, Juan Li, Rui-Quan Liao, Xin-Ming Cheng,
Multi-consensus of multi-agent networks via a rectangular impulsive approach,
Systems & Control Letters,
Volume 76,
2015,
Pages 28-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114002540)
Abstract: A multi-consensus problem is studied in multi-agent networks. The interaction mechanism of competition/abstention/cooperation among agents is introduced. Three rectangular impulsive protocols are proposed to solve multi-consensus of second order multi-agent networks with a directed topology. These algorithms have the performance of Dirac impulsive control and discrete-time control. Necessary and sufficient conditions are obtained for the stationary multi-consensus and the dynamic multi-consensus. Numerical examples are provided to illustrate the effectiveness of the obtained criteria.
Keywords: Multi-agent networks; Stationary multi-consensus; Dynamic multi-consensus; Rectangular impulsive approach

Nguyen Khoa Son, Do Duc Thuan, Nguyen Thi Hong,
Radius of approximate controllability of linear retarded systems under structured perturbations,
Systems & Control Letters,
Volume 84,
2015,
Pages 13-20,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115001528)
Abstract: In this paper we shall deal with the problem of calculation of the radius of approximate controllability in the Banach state space Kn×L2([−hk,0],Kn) for linear retarded systems of the form ẋ(t)=A0x(t)+A1x(t−h1)+⋯+Akx(t−hk)+Bu(t). By using multi-valued linear operators we are able to derive computable formulas for this radius when the system’s coefficient matrices are subjected to structured perturbations. Some examples are provided to illustrate the obtained results.
Keywords: Linear retarded systems; Approximate controllability; Multi-valued linear operators; Structured perturbations; Controllability radius

Da-Wei Ding, Heng Wang, Xiaoli Li,
H−/H∞ fault detection observer design for two-dimensional Roesser systems,
Systems & Control Letters,
Volume 82,
2015,
Pages 115-120,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.005.
(http://www.sciencedirect.com/science/article/pii/S0167691115000833)
Abstract: This paper addresses the problem of H−/H∞ fault detection for two-dimensional (2-D) systems with disturbances in Roesser model. A fault detection observer is designed to satisfy a finite frequency H− index and an H∞ index simultaneously. The finite frequency H− index is used to increase the fault sensitivity in low frequency domain while the H∞ index is used to attenuate the effects of disturbances in full frequency domain. By the generalized Kalman–Yakubovich–Popov lemma and some useful lemmas, sufficient design conditions are obtained. An example is given to illustrate the effectiveness of the proposed method.
Keywords: Fault detection; Two-dimensional systems; Roesser model; Finite frequency

Jun-Min Wang, Ling-Ling Su, Han-Xiong Li,
Stabilization of an unstable reaction–diffusion PDE cascaded with a heat equation,
Systems & Control Letters,
Volume 76,
2015,
Pages 8-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114002527)
Abstract: We consider a control problem of an unstable reaction–diffusion parabolic PDE cascaded with a heat equation through a boundary, where the heat influx of the heat equation is fed into the temperature of the reaction–diffusion equation, and the control actuator is designed at the another boundary of the heat equation. A backstepping invertible transformation is used to design a suitable boundary feedback control so that the closed-loop system is equivalent to a cascade of PDE–PDE system, which is shown to be exponentially stable in a suitable Hilbert space. With the Dirichlet boundary input from the heat equation, the reaction–diffusion PDE is shown to be exponentially stable in H−1(0,1). Numerical simulations are presented to illustrate the convergence of the state of the reaction–diffusion equation.
Keywords: Reaction–diffusion PDE; Heat equation; Backstepping; Stability

Qingbin Gao, Ayhan S. Kammer, Umut Zalluhoglu, Nejat Olgac,
Combination of sign inverting and delay scheduling control concepts for multiple-delay dynamics,
Systems & Control Letters,
Volume 77,
2015,
Pages 55-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.001.
(http://www.sciencedirect.com/science/article/pii/S016769111500002X)
Abstract: In this paper we treat a novel combination of two controversial control concepts, Sign Inverting Control (SIC) and Delay Scheduling (DS), for systems with multiple independent and large delays. SIC suggests the inversion of the control polarity and DS prolongs the existing delays. The combined scheme functions with a single requirement that, the union of the control schemes provides a larger stable operating region than each of its components does, in the domain of the delays. The critical knowledge that is needed to execute such a unified control strategy is the crisp description of these stable regions for each time-delayed control scheme. This need can be fulfilled using the recent Cluster Treatment of Characteristic Roots (CTCR) paradigm, which establishes the stable regions exhaustively and non-conservatively. The resulting options in selecting operating modes render more robust control performance against much larger delay variations than each of the schemes. We also investigate the disturbance rejection speeds within these enlarged stable regions in order to improve the control performance even further. Such multi-faceted paradoxical combinations provide previously-unexplored tools to control designers. Experimental validations of these novel concepts are presented on a simple setup with a single-axis manipulator.
Keywords: Sign-inverting control; Delay scheduling; Time-delayed systems; Stability analysis; Control performance; Delay robustness

Bin Zhang, Yingmin Jia,
Extensions of weak-invariance principle for nonlinear switched systems with time-invariant and time-varying subsystems,
Systems & Control Letters,
Volume 80,
2015,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.011.
(http://www.sciencedirect.com/science/article/pii/S016769111500078X)
Abstract: This paper addresses the stability problem for nonlinear switched systems with both time-invariant and time-varying subsystems. Given that Lyapunov-like functions are difficult to construct for nonlinear switched systems, generalized invariance principles are established based on observer functions. For nonlinear switched systems where the subsystems share Lyapunov-like functions, the generalized invariance principles can be specialized to Lyapunov-based invariance principles, where accurate convergent region can be obtained. In addition to the above efforts, the definitions of p-limit system and limit system set are presented, under which the proposed invariance principles are extended to nonlinear switched systems with time-varying subsystems. Illustrative examples show the effectiveness of the theoretical results.
Keywords: Nonlinear switched systems; Invariance principle; Dwell time; Observer function

Shuang Wu, Guangchen Wang,
Optimal control problem of backward stochastic differential delay equation under partial information,
Systems & Control Letters,
Volume 82,
2015,
Pages 71-78,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115001127)
Abstract: In this paper, we study the optimal control problem of backward stochastic differential delay equation under partial information. A class of time-advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. By means of ASDEs, we suggest a maximum principle of this problem and obtain necessary and sufficient conditions of optimality. We apply the theoretical results to study linear quadratic optimal control problem and obtain a forward–backward stochastic differential filtering equation (FBSDFE) with time-advanced forward equation that leads to optimal control. At the same time, some auxiliary filtering results and properties about time-advanced SDEs are also presented.
Keywords: Backward stochastic differential delay equation; Time-advanced stochastic differential equation; Maximum principle; Forward–backward stochastic differential filtering equation; Nonlinear filtering; Linear quadratic optimal control

A. Seuret, F. Gouaisbaut,
Hierarchy of LMI conditions for the stability analysis of time-delay systems,
Systems & Control Letters,
Volume 81,
2015,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115000675)
Abstract: Assessing stability of time-delay systems based on the Lyapunov–Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on an a priori design of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequalities which are asymptotically non conservative and then to design functionals driven by these inequalities. The resulting stability conditions form a hierarchy of LMI which is competitive with the most efficient existing methods (delay-partitioning, discretization and sum of squares), in terms of conservatism and of complexity. Finally, some examples show the efficiency of the method.
Keywords: Bessel’s inequality; Jensen’s inequality; Stability analysis; Time-delay systems; Lyapunov–Krasovskii functionals

Marco M. Nicotra, Roberto Naldi, Emanuele Garone,
Sufficient conditions for the stability of a class of second order systems,
Systems & Control Letters,
Volume 84,
2015,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115001401)
Abstract: This paper provides sufficient conditions to assess the stability and Input-to-State stability of a class of second-order systems by only looking at the structure of the dynamic equations. These results are proven by using the Variable Gradient Method to build suitable Lyapunov functions. The paper includes a number of relevant examples that highlight the value of the contribution.
Keywords: Second order systems; Variable gradient method; Input-to-state stability; Lyapunov stability

Onvaree Techakesari, Hendra I. Nurdin,
On the quasi-balanceable class of linear quantum stochastic systems,
Systems & Control Letters,
Volume 78,
2015,
Pages 25-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.010.
(http://www.sciencedirect.com/science/article/pii/S0167691115000201)
Abstract: This paper is concerned with the characterization of the quasi-balanceable class of linear quantum stochastic systems (i.e., systems that can be approximated via the recently proposed quasi-balanced truncation method). It has previously been shown that the quasi-balanceable class of systems includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. We derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.
Keywords: Linear quantum stochastic systems; Model reduction; Symplectic transformations; Quantum optical systems; Open Markov quantum systems

Ndolane Sene, Antoine Chaillet, Moussa Balde,
Relaxed conditions for the stability of switched nonlinear triangular systems under arbitrary switching,
Systems & Control Letters,
Volume 84,
2015,
Pages 52-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115001255)
Abstract: This paper addresses the stability of a class of nonlinear switching systems under arbitrary switching. It focuses on switching systems whose modes are made of a cascade of nonlinear scalar systems. It relaxes the stability conditions proposed by Angeli and Liberzon, by relying on the Strong iISS property which is known to be preserved under cascade interconnection. Its applicability is illustrated by the study of switched bilinear systems in triangular form.
Keywords: Nonlinear switching systems; Triangular systems; Stability analysis; Bilinear systems

Wojciech Paszke, Pawel Dabkowski, Eric Rogers, Krzysztof Gałkowski,
New results on strong practical stability and stabilization of discrete linear repetitive processes,
Systems & Control Letters,
Volume 77,
2015,
Pages 22-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114002771)
Abstract: Discrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. They arise in the modeling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a form of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and control law design algorithms for the strong practical stability property. Relative to alternatives, the LMIs for stability have a simpler structure and it is not required to impose particular structures on the matrix variables. These properties are extended to control law design, including those where state vector access is not required. Illustrative numerical simulation examples conclude the paper.
Keywords: Linear repetitive processes; Control law design; Kalman–Yakubovich–Popov lemma

Julia Emelianova, Pavel Pakshin, Krzysztof Gałkowski, Eric Rogers,
Stability of nonlinear discrete repetitive processes with Markovian switching,
Systems & Control Letters,
Volume 75,
2015,
Pages 108-116,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114002254)
Abstract: Repetitive processes are a class of 2D systems that operate over a subset of the upper-right quadrant of the 2D plane. Applications include iterative learning control where experimental verification has been reported based on a linear time-invariant model approximation of the dynamics. This paper considers discrete nonlinear repetitive processes with Markovian switching and applies, as one application, the resulting stability theory to iterative learning control for a class of networked systems where time-varying dynamics arise.
Keywords: Nonlinear repetitive processes; Markovian switching; Stability; Robust control; Iterative learning control

Guoqi Li, Changyun Wen, Wei Xing Zheng, Guangshe Zhao,
Iterative identification of block-oriented nonlinear systems based on biconvex optimization,
Systems & Control Letters,
Volume 79,
2015,
Pages 68-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.003.
(http://www.sciencedirect.com/science/article/pii/S0167691115000043)
Abstract: We investigate the identification of a class of block-oriented nonlinear systems which is represented by a common model in this paper. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. By applying the results to Hammerstein–Wiener systems with an invertible nonlinear function, the long-standing problem on the convergence of iteratively identifying such systems under arbitrary nonzero initial conditions is also now solved.
Keywords: Nonlinear system identification; Biconvex optimization; Parameter estimation; Hammerstein–Wiener model; Iterative method; Global minimum point

Weijun Cao, Jinhui Zhang, Wei Ren,
Leader–follower consensus of linear multi-agent systems with unknown external disturbances,
Systems & Control Letters,
Volume 82,
2015,
Pages 64-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.05.007.
(http://www.sciencedirect.com/science/article/pii/S0167691115001097)
Abstract: This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.
Keywords: Multi-agent systems; Leader–follower consensus; Distributed extended state observer

Wuquan Li,
Distributed output tracking of high-order nonlinear multi-agent systems with unstable linearization,
Systems & Control Letters,
Volume 83,
2015,
Pages 67-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.009.
(http://www.sciencedirect.com/science/article/pii/S0167691115001371)
Abstract: This paper addresses the problem of distributed output tracking for a class of high-order nonlinear multi-agent systems whose linearization parts may have unstable modes. For the case where the graph topology is directed and the leader is the neighbor of only a small portion of followers, distributed tracking control laws are designed. By using the algebra graph theory, it is shown that all the states of the closed-loop system are bounded, and the tracking errors can be tuned to be arbitrarily small. Finally, the design procedure is applied to underactuated unstable mechanical multi-agent systems, from which the efficiency of the tracking controllers is demonstrated.
Keywords: Nonlinear multi-agent systems; High-order; Unstable modes; Directed graph topology

Giuseppe Franzè, Walter Lucia,
The obstacle avoidance motion planning problem for autonomous vehicles: A low-demanding receding horizon control scheme,
Systems & Control Letters,
Volume 77,
2015,
Pages 1-10,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.12.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114002758)
Abstract: The paper addresses the obstacle avoidance motion planning problem for ground vehicles operating in uncertain environments. By resorting to set-theoretic ideas, a receding horizon control algorithm is proposed for robots modelled by linear time-invariant (LTI) systems subject to input and state constraints and disturbance effects. Sequences of inner ellipsoidal approximations of the exact one-step controllable sets are pre-computed for all the possible obstacle scenarios and then on-line exploited to determine the more adequate control action to be applied to the robot in a receding horizon fashion. The resulting framework guarantees Uniformly Ultimate Boundedness and constraints fulfilment regardless of any obstacle scenario occurrence.
Keywords: Obstacle avoidance; Set-theoretic approach; Receding horizon control; Constraint satisfaction

Franco Blanchini, Patrizio Colaneri, Yasumasa Fujisaki, Stefano Miani, Felice Andrea Pellegrino,
A Youla–Kučera parameterization approach to output feedback relatively optimal control,
Systems & Control Letters,
Volume 81,
2015,
Pages 14-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.04.006.
(http://www.sciencedirect.com/science/article/pii/S0167691115000845)
Abstract: This paper presents a continuous time solution to the problem of designing a relatively optimal control, precisely, a dynamic control which is optimal with respect to a given initial condition and is stabilizing for any other initial state. This technique provides a drastic reduction of the complexity of the controller and successfully applies to systems in which (constrained) optimality is necessary for some “nominal operation” only. The technique is combined with a pole assignment procedure. It is shown that once the closed-loop poles have been fixed and an optimal trajectory originating from the nominal initial state compatible with these poles is computed, a stabilizing compensator which drives the system along this trajectory can be derived in closed form. There is no restriction on the optimality criterion and the constraints. The optimization is carried out over a finite-dimensional parameterization of the trajectories. The technique has been presented for state feedback. We propose here a technique based on the Youla–Kučera parameterization which works for output feedback. The main result is that we provide conditions for solvability in terms of a set of linear algebraic equations.
Keywords: Relatively optimal control; Youla–Kučera parameterization; Output feedback; Continuous time systems

Jing Zeng, Jinfeng Liu,
Distributed moving horizon state estimation: Simultaneously handling communication delays and data losses,
Systems & Control Letters,
Volume 75,
2015,
Pages 56-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114002515)
Abstract: In this work, we consider distributed moving horizon state estimation of nonlinear systems subject to communication delays and data losses. In the proposed design, a local estimator is designed for each subsystem and the distributed estimators communicate to collaborate. To handle the delays and data losses simultaneously, a predictor is designed for each subsystem estimator. A two-step prediction-update strategy is used in the predictor design in order to get a reliable prediction of the system state. In the design of each subsystem estimator, an auxiliary nonlinear observer is also taken advantage of to calculate a reference subsystem state estimate. In the local estimator, the reference state estimate is used to generate a confidence region within which the local estimator optimizes its subsystem state estimate. Sufficient conditions under which the proposed design gives decreasing and ultimately bounded estimation error are provided. The effectiveness of the proposed approach is illustrated via the application to a chemical process example.
Keywords: Nonlinear systems; Distributed state estimation; Moving horizon estimation; Communication algorithms; Chemical processes

Javier A. Gallegos, Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, Rafael Castro-Linares,
On fractional extensions of Barbalat Lemma,
Systems & Control Letters,
Volume 84,
2015,
Pages 7-12,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115001413)
Abstract: This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.
Keywords: Fractional calculus; Asymptotics properties; Barbalat Lemma

M. Eulalia Montoro, Ferran Puerta, Xavier Puerta,
On the perturbation of bimodal control linear systems,
Systems & Control Letters,
Volume 80,
2015,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115000444)
Abstract: The aim of this paper is the study of local perturbations of a bimodal system which consists of two linear control systems on each side of a given hyperplane. We follow Arnold’s technique based on obtaining a miniversal deformation corresponding to the action of a group associated to a simultaneous feedback equivalence. An application to the study of the controllability of local perturbations of such a system is included.
Keywords: Bimodal system; Canonical form; Miniversal deformation

Guoqi Li, Changyun Wen, Aiming Zhang,
Fixed point iteration in identifying bilinear models,
Systems & Control Letters,
Volume 83,
2015,
Pages 28-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.06.008.
(http://www.sciencedirect.com/science/article/pii/S016769111500136X)
Abstract: Inspired by fixed point theory, an iterative algorithm is proposed to identify bilinear models recursively in this paper. It is shown that the resulting iteration is a contraction mapping on a metric space when the number of input–output data points approaches infinity. This ensures the existence and uniqueness of a fixed point of the iterated function sequence and therefore the convergence of the iteration. As an application, one class of block-oriented systems represented by a cascade of a dynamic linear (L), a static nonlinear (N) and a dynamic linear (L) subsystems is illustrated. This gives a solution to the long-standing convergence problem of iteratively identifying LNL (Winer–Hammerstein) models. In addition, we extend the static nonlinear function (N) to a nonparametric model represented by using kernel machine.
Keywords: Bilinear models; Wiener–Hammerstein models; LNL systems; Fixed point; Iterative algorithm; Contraction mapping; Kernel machine; Nonlinear systems identification

Diego Muñoz-Carpintero, Mark Cannon, Basil Kouvaritakis,
Robust MPC strategy with optimized polytopic dynamics for linear systems with additive and multiplicative uncertainty,
Systems & Control Letters,
Volume 81,
2015,
Pages 34-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.03.008.
(http://www.sciencedirect.com/science/article/pii/S0167691115000687)
Abstract: Polytopic dynamics have been introduced into the predictions in Model Predictive Control (MPC) and have been optimized so as to maximize invariant ellipsoids for systems subject to multiplicative uncertainty. This work was recently extended to the case of mixed additive and multiplicative uncertainty, and sufficient conditions were provided to guarantee the invariance of an ellipsoid. Additionally, under the assumption that the multiplicative uncertainty is known during a prediction horizon N, this extension was used as the terminal control law of an overall robust MPC strategy that deployed an affine-in-the-disturbance policy. This assumption was needed to enable the handling of constraints in the overall MPC strategy. The aims of this paper are to establish the necessity and sufficiency of the relevant invariance conditions of the polytopic dynamics, and to propose a robust MPC strategy that uses polytopic sets to describe the evolution of predicted variables and therefore does not make an assumption that future multiplicative uncertainty is known. The number of constraints and free variables of the resulting online optimization grows linearly with N. The benefits of the strategy are illustrated by numerical simulations.
Keywords: MPC; Robust control; Additive/multiplicative uncertainty; Optimized dynamics; Polytopic prediction sets

Salvatore Monaco, Dorothée Normand-Cyrot,
On optimality of passivity based controllers in discrete-time,
Systems & Control Letters,
Volume 75,
2015,
Pages 117-123,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114002242)
Abstract: The paper deals with connections between optimality and passivity-like properties in discrete time. The problem is set in the framework of differential/difference representations of discrete-time dynamics. The Hamilton–Jacobi–Bellman equality associated with a given cost and the corresponding optimal control solution are characterized. On these bases the connection with u-average passivity is clarified by exploiting the inverse optimal control problem associated with a given Lyapunov stabilizing feedback. Some constructive cases are analyzed.
Keywords: Nonlinear discrete-time systems; Optimal control; Nonlinear stabilization; Passivity based control; Lyapunov design

Yuan-Qing Wu, Hongye Su, Renquan Lu, Zheng-Guang Wu, Zhan Shu,
Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling,
Systems & Control Letters,
Volume 84,
2015,
Pages 35-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.08.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115001541)
Abstract: In this paper, the problem of non-fragile passive control for Markovian jump systems with aperiodic sampling is investigated. The considered controller is assumed to have either additive or multiplicative norm-bounded uncertainties. A time-dependent Lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non-fragile stochastic passivity of the resultant closed-loop system. Based on the condition, a mode-independent state feedback sampled-data controller is designed such that for all admissible uncertainties the closed-loop system is robustly stochastically passive. Two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques.
Keywords: Non-fragile control; Markovian jump systems; Sampled-data control

Qiang Yu, Baowei Wu,
Generalized Lyapunov function theorems and its applications in switched systems,
Systems & Control Letters,
Volume 77,
2015,
Pages 40-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.01.004.
(http://www.sciencedirect.com/science/article/pii/S0167691115000055)
Abstract: Generalized Lyapunov theorems of nonlinear systems are developed wherein all regularity assumptions on traditional Lyapunov function are removed. In particular, stability theorems of nonlinear systems are presented by replacing “V along the system trajectories is non-increasing” with “V along the system trajectories may increase its value during some proper time intervals”. Furthermore, stability theorems of discrete-time and continuous-time switched system with unstable subsystems are derived, using the generalized Lyapunov theorems. Two numerical examples are included to illustrate the effectiveness of the method.
Keywords: Generalized Lyapunov function; Nonlinear systems; Switched systems; Stability


Editorial Board,
Systems & Control Letters,
Volume 77,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00029-8.
(http://www.sciencedirect.com/science/article/pii/S0167691115000298)

D. Lam, C. Manzie, M.C. Good, R.R. Bitmead,
Receding horizon time-optimal control for a class of differentially flat systems,
Systems & Control Letters,
Volume 83,
2015,
Pages 61-66,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2015.07.001.
(http://www.sciencedirect.com/science/article/pii/S0167691115001383)
Abstract: A closed-loop, time-optimal path-following control scheme is proposed for a class of constrained differentially flat systems. Within a receding horizon framework, a finite horizon optimisation problem is solved at each sample, using available state feedback and feedforward path information. Irrespective of horizon length, the proposed formulation guarantees exact path-following. Moreover, the requirements under which the proposed algorithm achieves minimum-time path-following are established. Simulations conducted with a rigid X–Y table model confirm the theoretical results.
Keywords: Model predictive control; Time optimal control; Differentially flat systems

K.D. Do,
Global inverse optimal stabilization of stochastic nonholonomic systems,
Systems & Control Letters,
Volume 75,
2015,
Pages 41-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114002369)
Abstract: Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems. This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize (in probability) nonholonomic systems affine in stochastic disturbances. The design is based on the Lyapunov direct method, the backstepping technique, and the inverse optimal control design. A class of Lyapunov functions, which are not required to be as nonlinearly strong as quadratic or quartic, is proposed for the control design. Thus, these Lyapunov functions can be applied to design of controllers for underactuated (stochastic) mechanical systems, which are usually required Lyapunov functions of a nonlinearly weak form. The proposed control design is illustrated on a kinematic cart, of which wheel velocities are perturbed by stochastic noise.
Keywords: Stochastic nonholonomic systems; Global stabilization; Inverse optimal


Editorial Board,
Systems & Control Letters,
Volume 81,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(15)00114-0.
(http://www.sciencedirect.com/science/article/pii/S0167691115001140)

Rafael Vazquez, Miroslav Krstic,
Marcum Q-functions and explicit kernels for stabilization of 2×2 linear hyperbolic systems with constant coefficients,
Systems & Control Letters,
Volume 68,
2014,
Pages 33-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114000607)
Abstract: We find the exact analytical solution to a Goursat PDE system governing the kernels of a backstepping-based boundary control law that stabilizes a constant-coefficient 2×2 system of first-order hyperbolic linear PDEs. The solution to the Goursat system is related to the solution of a simpler, explicitly solvable Goursat system through a suitable infinite series of powers of partial derivatives which is summed explicitly in terms of special functions, including Bessel functions and the generalized Marcum Q-functions of the first order. The Marcum functions are common in certain applications in communications but have not appeared previously in control design problems. The dependence of the explicit solutions with respect to system parameters is analyzed through several examples, including the stabilization of a constant equilibrium for a quasi-linear plant.
Keywords: Partial differential equations; Marcum generalized Q-function; Infinite-dimensional systems; Backstepping; Hyperbolic systems; Constant coefficients; Control kernels

Paul Trodden,
Feasible parallel-update distributed MPC for uncertain linear systems sharing convex constraints,
Systems & Control Letters,
Volume 74,
2014,
Pages 98-107,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.012.
(http://www.sciencedirect.com/science/article/pii/S0167691114001819)
Abstract: A distributed MPC approach for linear uncertain systems sharing convex constraints is presented. The systems, which are dynamically decoupled but share constraints on state and/or inputs, optimize once, in parallel, at each time step and exchange plans with neighbours thereafter. Coupled constraint satisfaction is guaranteed, despite the simultaneous decision making, by extra constraint tightening in each local problem. Necessary and sufficient conditions are given on the margins for coupled constraint satisfaction, and a simple on-line scheme for selecting margins is proposed that satisfies the conditions. Robust feasibility and stability of the overall system are guaranteed by use of the tube MPC concept in conjunction with the extra coupled constraint tightening.
Keywords: Control of constrained systems; Predictive control; Decentralization; Time-invariant

E. Bakolas,
Decentralized spatial partitioning algorithms for multi-vehicle systems based on the minimum control effort metric,
Systems & Control Letters,
Volume 73,
2014,
Pages 81-87,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114001777)
Abstract: We consider the problem of characterizing a spatial partition of the position space of a team of vehicles with linear time-varying kinematics. The generalized metric that determines the proximity relations between the vehicles and an arbitrary target point in the partition space is the minimum control effort required for each vehicle to reach the latter point with zero miss distance and exactly zero velocity at a prescribed final time. We show that the solution to the generalized Voronoi partitioning problem can be associated with a special class of spatial partitions known as affine diagrams. Because the combinatorial complexity of the affine diagrams is comparable to the one of the standard Voronoi diagrams, their computation does not pose a significant challenge in applications of multi-vehicle systems. Subsequently, we propose an algorithm for the computation of the spatial partition, which is decentralized in the sense that each vehicle can compute an approximation of its own cell independently from the other vehicles from the same team without utilizing a common spatial mesh. Numerical simulations that illustrate the theoretical developments are also presented.
Keywords: Voronoi diagrams; Spatial partitioning; Multi-vehicle systems; Minimum control effort

Ke-Cai Cao, Bin Jiang, Dong Yue,
Consensus of multiple nonholonomic chained form systems,
Systems & Control Letters,
Volume 72,
2014,
Pages 61-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114001534)
Abstract: Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.
Keywords: Consensus; Nonholonomic system; Persistent excitation; Cascaded systems

Henrik Sandberg, Per Hägg, Bo Wahlberg,
Approximative model reconstruction of cascade systems,
Systems & Control Letters,
Volume 69,
2014,
Pages 90-97,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114001017)
Abstract: This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data.
Keywords: Model reduction; Cascade systems; Model matching


Editorial Board,
Systems & Control Letters,
Volume 71,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00166-2.
(http://www.sciencedirect.com/science/article/pii/S0167691114001662)

Xianwei Li, James Lam, Huijun Gao, Ping Li,
Improved results on H∞ model reduction for Markovian jump systems with partly known transition probabilities,
Systems & Control Letters,
Volume 70,
2014,
Pages 109-117,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.012.
(http://www.sciencedirect.com/science/article/pii/S0167691114001145)
Abstract: This paper is concerned with the model reduction problem for Markovian jump systems with partly known transition probabilities. By making use of an existing result on the convex properties of the transition probabilities, an improved condition is first derived for the H∞ performance analysis of the error system. Two different approaches, one in terms of linear matrix inequalities (LMIs) and another in the form of an iterative algorithm subject to LMI constraints, are then proposed to find a reduced-order model such that the H∞ performance of the error system is bounded by a specified level. The first approach is obtained using Finsler’s Lemma, and involves fewer decision variables than the existing method. It is shown that the proposed methods cover some existing results as special cases. Finally, the advantages of our results are clearly illustrated by a numerical example.
Keywords: Model reduction; H∞ performance; Markovian jump systems; Partly known transition probabilities (PKTPs)

Samuel Martin,
Multi-agent flocking under topological interactions,
Systems & Control Letters,
Volume 69,
2014,
Pages 53-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114000851)
Abstract: In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by the so-called topological interaction rule: agents interact with a fixed number of their closest neighbors. This rule comes from observations of real flock of starlings. The non-symmetry of the interactions adds to the difficulty of the analysis. The goal of this paper is to determine practical conditions (on the initial positions and velocities of agents) ensuring that the agents asymptotically agree on a common velocity (i.e. a flocking behavior is achieved). For this purpose, we define a notion of hierarchical structure in the interaction graph which allows to establish such conditions, building upon previous work on multi-agent systems with switching communication networks. Though conservative, our approach gives conditions that can be verified a priori. Our result is illustrated through simulations.
Keywords: Topological interactions; Flocking; Multi-agent systems

Isuru S. Dasanayake, Jr-Shin Li,
Constrained charge-balanced minimum-power controls for spiking neuron oscillators,
Systems & Control Letters,
Volume 75,
2015,
Pages 124-130,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114002072)
Abstract: In this paper, we study the optimal control of phase models for spiking neuron oscillators. We focus on the design of minimum-power current stimuli that elicit spikes of neurons at specified times, subject to the charge-balance constraint. Such charge-balanced controls, in practice, are used to suppress undesirable side effects occurred due to the accumulation of electric charge resulting from the applied external stimuli. We derive charge-balanced minimum-power controls for a general phase model using the maximum principle, where the cases with unbounded and bounded control amplitude are examined. The latter is of fundamental importance because phase models are valid under weak forcing. The developed optimal control strategies are applied to both mathematically ideal and experimentally observed phase models to demonstrate their applicability, including the widely studied Hodgkin–Huxley model.
Keywords: Spiking neurons; Phase models; Phase response curve (PRC); Optimal control; Maximum principle

Xuerong Mao, Wei Liu, Liangjian Hu, Qi Luo, Jianqiu Lu,
Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations,
Systems & Control Letters,
Volume 73,
2014,
Pages 88-95,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114001807)
Abstract: Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ. Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.
Keywords: Brownian motion; Markov chain; Mean-square exponential stability; Feedback control; Discrete-time state observation

Matthew C. Turner, Murray Kerr,
Lyapunov functions and L2gain bounds for systems with slope restricted nonlinearities,
Systems & Control Letters,
Volume 69,
2014,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114000838)
Abstract: The stability and L2performance analysis of systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static nonlinear element which is Lipschitz, slope restricted and sector bounded is revisited. The main thrust of the paper is to improve and extend an existing result in the literature to enable (i) concise and correct conditions for asymptotic stability of the interconnection and (ii) reasonably tight bounds on the L2gain between an exogenous input and a given output to be obtained. Numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature.
Keywords: Saturation; Anti-windup; Absolute stability

Patrik Axelsson, Rickard Karlsson, Mikael Norrlöf,
Estimation-based norm-optimal iterative learning control,
Systems & Control Letters,
Volume 73,
2014,
Pages 76-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114001765)
Abstract: The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.
Keywords: Iterative learning control; Estimation; Filtering; Non-linear systems

Jamal Daafouz, Marius Tucsnak, Julie Valein,
Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line,
Systems & Control Letters,
Volume 70,
2014,
Pages 92-99,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.009.
(http://www.sciencedirect.com/science/article/pii/S016769111400111X)
Abstract: We consider an infinite dimensional system modeling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations modeling the converter. The coupling is given by the boundary conditions and the nonlinear controller we introduce. We design a nonlinear saturating control law using a Lyapunov function for the averaged model of the system. The main results give the well-posedness and stability properties of the obtained closed loop system.
Keywords: Infinite dimensional system; Telegraph equations; Power converters; Stabilization; Coupled system

Paolo Massioni,
Distributed control for alpha-heterogeneous dynamically coupled systems,
Systems & Control Letters,
Volume 72,
2014,
Pages 30-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114001649)
Abstract: This paper concerns the problem of distributed controller synthesis for a class of heterogeneous distributed systems composed of α (2 or more) different kinds of subsystems, interacting with one another according to a certain given graph topology. We will show that by employing Linear Matrix Inequalities (LMIs) tools, namely the full-block S-procedure, we can derive a control synthesis method based on L2 gain performance. This synthesis method guarantees stability and performance of a whole set of possible interconnection graphs, and its computational complexity does not depend on the number of subsystems involved but only on the number of different kinds of subsystems. The effectiveness of the new method is verified on a test case.
Keywords: Distributed control; Heterogeneous systems

Xiaofeng Su, Yingmin Jia,
Self-scheduled robust decoupling control with H∞ performance of hypersonic vehicles,
Systems & Control Letters,
Volume 70,
2014,
Pages 38-48,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114001133)
Abstract: This paper is concerned with self-scheduled robust decoupling control for hypersonic vehicles subject to both parameter uncertainty and external disturbance. The overall design procedure includes three loops to be closed in sequence, where the robust decoupling of the middle-loop system is most important and challenging. The decoupling problem of middle loop is firstly reformulated as the robust H∞ control of a general uncertain linear parameter-varying (LPV) error system, in which the parameters are the command signals. Then, through transforming the robust H∞ problem of the uncertain LPV error system into a certain one, the tensor-product (TP) model transformation technique can be directly employed to obtain a convex polytopic form, which greatly decreases the computing load of the controller design. Hence, the controller is obtained by solving limited number of linear matrix inequalities (LMIs) corresponding to the vertex systems. The resulting controller is time-varying and self-scheduled. Moreover, the decoupling is guaranteed against parameter uncertainty, whereas approximate decoupling can only be achieved when an external disturbance exists. Nevertheless, the degree of approximate decoupling can be enhanced by choosing a small performance index γ. The efficacy of the proposed method is supported by simulations.
Keywords: Hypersonic vehicles; Decoupling control; Linear parameter-varying system; Robust H∞ theory

M. Baglietto, G. Battistelli, P. Tesi,
Mode-observability degree in discrete-time switching linear systems,
Systems & Control Letters,
Volume 70,
2014,
Pages 69-76,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.006.
(http://www.sciencedirect.com/science/article/pii/S016769111400108X)
Abstract: In this paper, we consider the problem of identifying the active mode of a switching linear system from data sequences of a finite length. The results combine elements from canonical correlation analysis and subspace projection methods. In addition to providing insight into the geometric meaning of the problem, the results turn out to be of practical relevance whenever mode-identification is addressed in the presence of noisy-corrupted measurements. In particular, the results can be used to provide conditions under which mode-identification occurs independently of a prescribed noise level.
Keywords: Switching systems; Mode observability; Mode estimation

Lorenzo Ntogramatzidis, Augusto Ferrante,
The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure,
Systems & Control Letters,
Volume 75,
2015,
Pages 84-93,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114002345)
Abstract: In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that it is an explicit expression of the addend X0 which is common to all solutions, so that it does not depend on the particular X. The second part can be–depending on the structure of the considered generalized Riccati equation–either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
Keywords: Generalized Riccati equations

Insoon Yang, Claire J. Tomlin,
Reaction–diffusion systems in protein networks: Global existence and identification,
Systems & Control Letters,
Volume 74,
2014,
Pages 50-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.013.
(http://www.sciencedirect.com/science/article/pii/S0167691114002102)
Abstract: Spatio-temporal biochemical signaling in a large class of protein–protein interaction networks is well modeled by a reaction–diffusion system. The global existence of the solution to the reaction–diffusion system is determined by the reaction kinetics model and the protein network topology. We propose a novel reaction kinetics model that guarantees that the reaction–diffusion system with this model has a nonnegative invariant global classical solution for any network topology. We then present a computational method to identify the unknown parameters and initial values for a reaction–diffusion system with this reaction kinetics model. The identification approach solves an optimization problem that minimizes the cost function defined as the L2-norm of the difference between the data and the solution of the reaction–diffusion system. We utilize an adjoint-based optimal control method to obtain the gradients of the cost function with respect to the parameters and initial values. The regularity of the global classical solutions of the reaction–diffusion system and its corresponding adjoint system avoids situations in which the gradients blow up, and therefore guarantees the success of the identification method for any network structure. Utilizing this gradient information, an efficient algorithm to solve the optimization problem is proposed and applied to estimate the mass diffusivities, rate constants and initial values of a reaction–diffusion system that models protein–protein interactions in a signaling network that regulates the actin cytoskeleton in a malignant breast cell.
Keywords: Reaction–diffusion systems; Global classical solution; Identification; Protein networks; Cancer systems biology

Xiwang Dong, Fanlin Meng, Zongying Shi, Geng Lu, Yisheng Zhong,
Output containment control for swarm systems with general linear dynamics: A dynamic output feedback approach,
Systems & Control Letters,
Volume 71,
2014,
Pages 31-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114001376)
Abstract: Output containment control problems for high-order linear time-invariant swarm systems under directed interaction topologies are investigated using a dynamic output feedback approach. Firstly, to propel the outputs of followers to converge to the convex hull formed by the outputs of leaders, a dynamic output containment protocol is presented. Then necessary and sufficient conditions for swarm systems to achieve output containment are proposed. To ensure the scalability of the criteria, a sufficient condition which only includes two linear matrix inequality constraints independent of the number of agents is further presented. Moreover, an approach independent of the number of agents is proposed to determine the gain matrices in the dynamic output containment protocols. Finally, numerical simulations are presented to demonstrate theoretical results.
Keywords: Output containment; High-order; Swarm system; Dynamic output feedback

Guojie Zheng, Bao-Zhu Guo, M. Montaz Ali,
Stability of optimal control of heat equation with singular potential,
Systems & Control Letters,
Volume 74,
2014,
Pages 18-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114002060)
Abstract: In this paper, we study stability of an optimal control for a multi-dimensional heat equation with a singular potential term. A family of perturbed optimal control problems with lower power singular potentials are formulated. It is shown that when the lower powers tend to the critical power two, the optimal controls are convergent to the optimal control of the original system.
Keywords: Heat equation; Singular potential; Optimal control; Sensitivity analysis

Roman Geiselhart, Rob H. Gielen, Mircea Lazar, Fabian R. Wirth,
An alternative converse Lyapunov theorem for discrete-time systems,
Systems & Control Letters,
Volume 70,
2014,
Pages 49-59,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114001091)
Abstract: This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov functions on a set [a,b] with 0<a<b<∞ are derived. Furthermore, for specific classes of systems, the developed converse Lyapunov theorem can be used to establish non-conservatism of existence of a particular type of Lyapunov functions. Most notably, a proof that the existence of conewise linear Lyapunov functions is non-conservative for GES conewise linear systems is given and, as a by-product, tractable construction of polyhedral Lyapunov functions for linear systems is attained.
Keywords: Discrete-time systems; Conewise linear systems; Stability analysis; Converse Lyapunov theorems

Karine Beauchard, Jean-Michel Coron, Holger Teismann,
Minimal time for the bilinear control of Schrödinger equations,
Systems & Control Letters,
Volume 71,
2014,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114001492)
Abstract: We consider a quantum particle in a potential V(x) (x∈RN) subject to a (spatially homogeneous) time-dependent electric field E(t), which plays the role of the control. Under generic assumptions on V, this system is approximately controllable on the L2(RN,C)-sphere, in sufficiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti (2012). In the present article, we show that this approximate controllability result is false in small time. As a consequence, the result by Boscain et al. is, in some sense, optimal with respect to the control time T.
Keywords: Schrödinger equation; Quantum control; Minimal time

Giorgio Battistelli, Daniele Mari, Daniela Selvi, Alberto Tesi, Pietro Tesi,
Adaptive disturbance attenuation via logic-based switching,
Systems & Control Letters,
Volume 73,
2014,
Pages 48-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114001996)
Abstract: The problem of attenuating unknown and possibly time-varying disturbances acting on a linear time-invariant dynamical system is addressed by means of an adaptive switching control approach. Given a family of pre-designed stabilizing controllers, a supervisory unit infers in real-time the potential behavior of each candidate controller and selects the one providing the best potential performance. To this aim, a set of test functionals is defined, which is shown to enjoy favorable inference properties under certain assumptions on the nature of the disturbances. Both persistent-memory and finite-memory test functionals are analyzed. Further, an implementation of the switching controller is proposed which always guarantees stability of the feedback loop, even if the disturbance characteristics are such that the switching is persistent. Simulation results are provided to show the effectiveness of the proposed method.
Keywords: Adaptive control; Switching control; Adaptive disturbance attenuation

Masaki Ogura, Clyde F. Martin,
Stability analysis of linear systems subject to regenerative switchings,
Systems & Control Letters,
Volume 75,
2015,
Pages 94-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.009.
(http://www.sciencedirect.com/science/article/pii/S016769111400231X)
Abstract: This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the spectral radius of a matrix. The matrix is obtained by taking the expectation of the transition matrix of the system on one cycle of the underlying regenerative process. The characterization generalizes Floquet’s theorem for the stability analysis of linear time-periodic systems. We illustrate the result with the stability analysis of a linear system with a failure-prone controller under periodic maintenance.
Keywords: Switched linear system; Regenerative process; Mean stability; Periodic maintenance

Anne-Kathrin Schmuck, Jörg Raisch,
Asynchronous l-complete approximations,
Systems & Control Letters,
Volume 73,
2014,
Pages 67-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114001637)
Abstract: This paper extends the l-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous l-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and l-completeness is introduced, extending the behavioral systems theory in a consistent way.
Keywords: Finite state abstraction; l-complete approximations; State property; Behavioral systems theory

G.A. Leonov,
Pyragas stabilizability via delayed feedback with periodic control gain,
Systems & Control Letters,
Volume 69,
2014,
Pages 34-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114000826)
Abstract: In this paper for the unstable periodic solution of nonlinear differential equation, Pyragas stabilizability problem is studied. An algorithm of stabilization via periodical delayed feedback is obtained. The consideration is based on the theory of nonstationary stabilization.
Keywords: Stabilization; Delayed feedback control of chaos; Linearization; Floquet theorem; Pyragas method

Nicolas Boumal, Xiuyuan Cheng,
Concentration of the Kirchhoff index for Erdős–Rényi graphs,
Systems & Control Letters,
Volume 74,
2014,
Pages 74-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.006.
(http://www.sciencedirect.com/science/article/pii/S016769111400228X)
Abstract: Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the so-called Kirchhoff index of the graph, which measures its overall connectivity. In this work, we consider Erdős–Rényi random graphs. Since the graphs are random, their Kirchhoff indices are random variables. We give formulas for the expected value of the Kirchhoff index and show it concentrates around its expectation. We achieve this by studying the trace of the pseudoinverse of the Laplacian of Erdős–Rényi graphs. For synchronization (a class of estimation problems on graphs) our results imply that acquiring pairwise measurements uniformly at random is a good strategy, even if only a vanishing proportion of the measurements can be acquired.
Keywords: Resistance distance; Kirchhoff index; Erdős–Rényi; Estimation on graphs; Synchronization; Cramér–Rao bounds; Pseudoinverse of graph Laplacian; Random matrices; Sensor network localization

Ghazal Montaseri, Aras Adhami-Mirhosseini, Mohammad Javad Yazdanpanah,
Desynchronization of coupled limit-cycle oscillators through nonlinear output regulation,
Systems & Control Letters,
Volume 71,
2014,
Pages 38-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114001364)
Abstract: Synchronization is one of the most important phenomena in coupled oscillators. However, sometimes synchronization may be harmful and suppression of collective synchrony or desynchronization is desired. In this paper, we propose a control strategy for the desynchronization of an ensemble of all-to-all coupled Stuart–Landau oscillators. First, the desynchronization problem is redefined in the nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces Stuart–Landau oscillators (as a paradigm for limit-cycle oscillators) to track exogenous sinusoidal references with different phases. Finally, by considering some modifications, the initial version of the controller is improved to be more applicable in neuronal ensembles as an application of the desynchronization problem. The proposed stimulation is robust against variations of oscillators’ frequencies and can adapt itself with variations of the coupling strength. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.
Keywords: Nonlinear output regulation; Stuart–Landau oscillators; Suppress synchrony

Chuanrui Wang, Haibo Ji,
Leader-following consensus of multi-agent systems under directed communication topology via distributed adaptive nonlinear protocol,
Systems & Control Letters,
Volume 70,
2014,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114001121)
Abstract: In this paper, we study the leader-following consensus problem of general linear multi-agent systems under directed communication topology. To avoid using any global information, an adaptive nonlinear protocol is proposed based only on the relative state information. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. A numerical example is provided to illustrate the effectiveness of the theoretical results.
Keywords: Multi-agent systems; Leader-following consensus; Nonlinear algorithm; Adaptive control

S. Garatti,
A counterexample to the uniqueness of the asymptotic estimate in ARMAX model identification via the correlation approach,
Systems & Control Letters,
Volume 74,
2014,
Pages 14-17,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114002059)
Abstract: This paper deals with the identifiability of an ARMAX system when the correlation approach is adopted. In general, identifiability depends on both the parametrization of the model class and on the informativeness of the data. Here, we focus on the latter aspect and, therefore, a full-order model class is considered. The main goal is to provide a counterexample to the uniqueness of the asymptotic estimate when a persistently exciting input is adopted. This shows the somehow counterintuitive fact that the identifiability of ARMAX systems within the correlation approach is related to the “color” of the input.
Keywords: System identification; Correlation approach; Identifiability; Informative experiment

Felix Antritter, Franck Cazaurang, Jean Lévine, Johannes Middeke,
On the computation of π-flat outputs for linear time-varying differential-delay systems,
Systems & Control Letters,
Volume 71,
2014,
Pages 14-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114001522)
Abstract: We introduce a new definition of π-flatness for linear differential-delay systems with time-varying coefficients. We characterize π- and π-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present an academic example of motion planning to discuss the pertinence of the approach.
Keywords: Linear time-varying system; Differential-delay system; Differential flatness; π-flatness; Ore polynomials; Motion planning; Modules

Shiping Yang, Jian-Xin Xu, Deqing Huang, Ying Tan,
Optimal iterative learning control design for multi-agent systems consensus tracking,
Systems & Control Letters,
Volume 69,
2014,
Pages 80-89,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114001005)
Abstract: Under a repeatable operation environment, this paper proposes an iterative learning control scheme that can be applied to multi-agent systems to perform consensus tracking under the fixed communication topology. The agent dynamics are modeled by time-varying nonlinear equations which satisfy the global Lipschitz continuous condition. In addition, the desired consensus trajectory is only accessible to a subset of the followers. By using the concept of the graph dependent matrix norm, the convergence conditions can be specified at the agent level, which depend on a set of eigenvalues that are associated with the communication topology. The results are first derived for homogeneous agent systems and then extended to heterogeneous systems. Next, optimal controller gain design methods are proposed in the sense that the λ-norm of tracking error converges at the fastest rate, which imposes a tightest bounding function for the actual tracking error in the λ-norm analysis framework. In the end, an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods.
Keywords: Iterative learning control; Consensus tracking; Multi-agent systems; Optimal design

Jianhui Huang, Zhiyong Yu,
Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems,
Systems & Control Letters,
Volume 68,
2014,
Pages 68-75,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114000796)
Abstract: A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.
Keywords: Stochastic Riccati equation; Stochastic linear quadratic optimal control; Backward stochastic differential equation (BSDE)

Hui Zhang, Yuanqing Xia,
Instability of stochastic switched systems,
Systems & Control Letters,
Volume 75,
2015,
Pages 101-107,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114002291)
Abstract: The instability problem of stochastic switched systems is investigated in this paper. Definitions of instability are given in the forms of instability in probability, mth instability, moment exponential instability and almost sure exponential instability. By the aid of Dynkin’s formula, Itô’s formula and strong law of large numbers, the criteria on instability of stochastic switched systems under arbitrary switching are established based on Lyapunov-like techniques. Simulation examples are presented to illustrate the validity of the results.
Keywords: Stochastic instability; Switched systems; Stochastic systems

Deming Yuan, Daniel W.C. Ho, Shengyuan Xu,
Inexact dual averaging method for distributed multi-agent optimization,
Systems & Control Letters,
Volume 71,
2014,
Pages 23-30,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114001480)
Abstract: We consider a distributed convex optimization problem over a network where multiple agents collectively try to minimize a sum of local convex functions of the same variables, each of which is available to one specific agent only. For solving this optimization problem, we present an inexact version of the dual averaging method. This extends recent results of Duchi (2012), which cover the error-free case, to the case where an error is present in calculating the subgradient of the objective function or in computing the projection. We show that when the errors decrease at appropriate rates, our method achieves the same convergence rate as in the error-free case. In particular, the convergence of the method is also established for nonsummable errors. We also provide numerical results to validate the theoretic results.
Keywords: Convex optimization; Multi-agent systems; Distributed optimization; Dual averaging methods; Average consensus

Annika Eichler, Herbert Werner,
Closed-form solution for optimal convergence speed of multi-agent systems with discrete-time double-integrator dynamics for fixed weight ratios,
Systems & Control Letters,
Volume 71,
2014,
Pages 7-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114001509)
Abstract: This paper considers the convergence speed of multi-agent systems with discrete-time double-integrator dynamics. The communication topology is assumed to be fixed and undirected. The speed of convergence of the associated average consensus protocol is analyzed, and the problem of maximizing the convergence speed over the free parameters in the consensus protocol is considered. A closed-form solution to this problem is proposed assuming that the ratios of weights of communication links are fixed. Furthermore it is shown that when the weight ratios are considered as decision variables, a global optimum of the convergence speed can be obtained by solving an LMI problem. Simulation results are provided that demonstrate the effectiveness of the proposed approach.
Keywords: Multi-agent systems; Consensus problem; Consensus speed; Discrete-time systems; Double-integrator dynamics; Graph Laplacians

Zbigniew Bartosiewicz,
Positive nonlinear realizations of response maps,
Systems & Control Letters,
Volume 72,
2014,
Pages 7-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114001625)
Abstract: The problem of realization of a positive response map as a positive initialized system on a finite dimensional Euclidean state space is investigated. The dynamical part of the system is described by a delta differential equation on an arbitrary time scale. This incorporates continuous- and discrete-time systems. The main result states necessary and sufficient conditions for existence of positive realization of a particular class. The criterion is expressed in the language of skew differential global universes.
Keywords: Nonlinear positive system; Response map; Realization; Time scale; Observation universe; Skew differential universe

Fabio Morbidi, Alain Y. Kibangou,
A distributed solution to the network reconstruction problem,
Systems & Control Letters,
Volume 70,
2014,
Pages 85-91,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114001108)
Abstract: It has been recently shown in Ren et al. (2010) that by collecting noise-contaminated time series generated by a coupled-oscillator system at each node of a network, it is possible to robustly reconstruct its topology, i.e. determine the graph Laplacian. Restricting ourselves to linear consensus dynamics over undirected communication networks, in this paper we introduce a new dynamic average consensus least-squares algorithm to locally estimate these time series at each node, thus making the reconstruction process fully distributed and more easily applicable in the real world. We also propose a novel efficient method for separating the off-diagonal entries of the reconstructed Laplacian, and examine several concepts related to the trace of the dynamic correlation matrix of the coupled single integrators, which is a distinctive element of our network reconstruction method. The theory is illustrated with examples from computer, power and transportation systems.
Keywords: Network reconstruction; Consensus algorithms; Distributed estimation; Networked systems

Xuehong Zhu,
The optimal control related to Riemannian manifolds and the viscosity solutions to Hamilton–Jacobi–Bellman equations,
Systems & Control Letters,
Volume 69,
2014,
Pages 7-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114000814)
Abstract: In this paper we study the optimal stochastic control problem for stochastic differential equations on Riemannian manifolds. The cost functional is specified by controlled backward stochastic differential equations in Euclidean space. Under some suitable assumptions, we conclude that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation which is a fully nonlinear parabolic partial differential equation on Riemannian manifolds.
Keywords: Riemannian manifold; Hamilton–Jacobi–Bellman equation; Backward stochastic differential equations; Dynamic programming principle; Viscosity solution

Farhad Farokhi, Karl H. Johansson,
Adaptive control design under structured model information limitation: A cost-biased maximum-likelihood approach,
Systems & Control Letters,
Volume 75,
2015,
Pages 8-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114002321)
Abstract: Networked control strategies based on limited information about the plant model usually result in worse closed-loop performance than optimal centralized control with full plant model information. Recently, this fact has been established by utilizing the concept of competitive ratio, which is defined as the worst-case ratio of the cost of a control design with limited model information to the cost of the optimal control design with full model information. We show that an adaptive controller, inspired by a controller proposed by Campi and Kumar, with limited plant model information, asymptotically achieves the closed-loop performance of the optimal centralized controller with full model information for almost any plant. Therefore, there exists, at least, one adaptive control design strategy with limited plant model information that can achieve a competitive ratio equal to one. The plant model considered in the paper belongs to a compact set of stochastic linear time-invariant systems and the closed-loop performance measure is the ergodic mean of a quadratic function of the state and control input.
Keywords: Interconnected systems; Adaptive control; Optimal control; Structural constraints

Andrea Boccia, Lars Grüne, Karl Worthmann,
Stability and feasibility of state constrained MPC without stabilizing terminal constraints,
Systems & Control Letters,
Volume 72,
2014,
Pages 14-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114001595)
Abstract: In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N. For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel.
Keywords: Predictive control; Optimal control; Nonlinear control; Linear systems; Stability; State constraints; Feasibility; Optimal value functions

Joaquin Carrasco, Martin Maya-Gonzalez, Alexander Lanzon, William P. Heath,
LMI searches for anticausal and noncausal rational Zames–Falb multipliers,
Systems & Control Letters,
Volume 70,
2014,
Pages 17-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114001078)
Abstract: Given a linear time-invariant plant, the search for a suitable multiplier over the class of Zames–Falb multipliers is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames–Falb multipliers. This letter analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers. The addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search. As a result, a search over a noncausal subset of Zames–Falb multipliers is obtained. A comparison between all the search methods proposed in the literature is given.
Keywords: Slope-restricted nonlinearities; Zames–Falb multipliers; Multiplier search

Hyun-Wook Jo, Ho-Lim Choi, Jong-Tae Lim,
Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain,
Systems & Control Letters,
Volume 71,
2014,
Pages 44-53,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114001352)
Abstract: We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.
Keywords: Feedforward nonlinear system; Uncertain input and state delay; Adaptive gain-scaling factor; Output feedback

Chao Huang, Xudong Ye,
Pairwise synchronization of multi-agent systems with nonuniform information exchange,
Systems & Control Letters,
Volume 74,
2014,
Pages 58-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114002047)
Abstract: In this note, the pairwise output synchronization problem of heterogeneous linear multi-agent systems is proposed. Considering a pair of agents denoted by (i,j), the control objective of this problem is to achieve output synchronization between jth output of agent i and ith output of agent j, and for this reason it can be viewed as a generalization of existing works in the output synchronization literature. The communication network is undirected and time varying with relative output information available for intercommunication. When the agent dynamics are identical and the output signals are observable, this problem becomes a state synchronization problem with nonuniform information exchange, and our results show that state synchronization is achievable in jointly connected graph.
Keywords: Multi-agent systems; Synchronization; Passivity; Jointly-connected

Akaninyene Udo Udom,
Stabilization in probability and mean square of controlled stochastic dynamical system with state delay,
Systems & Control Letters,
Volume 68,
2014,
Pages 95-100,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114000784)
Abstract: Although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies, so far there are few works on controlled stochastic dynamical systems with state delay. In this paper, a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered. Condition under which the system is exponentially stable in mean square and in probability is examined.
Keywords: Delay; Exponential stability; Mean square stability; Stochastic dynamical system; Optimal control

Chongyang Liu, Ryan Loxton, Kok Lay Teo,
A computational method for solving time-delay optimal control problems with free terminal time,
Systems & Control Letters,
Volume 72,
2014,
Pages 53-60,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114001510)
Abstract: This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.
Keywords: Time-delay system; Optimal control; Free terminal time; Control parameterization; Nonlinear optimization

Dapeng Yang, Wei Ren, Xiangdong Liu,
Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems,
Systems & Control Letters,
Volume 72,
2014,
Pages 44-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.006.
(http://www.sciencedirect.com/science/article/pii/S016769111400156X)
Abstract: In this paper, we study the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph. We first propose a fully distributed adaptive sliding-mode control algorithm combined with distributed sliding-mode estimators, without requiring the upper bounds of the derivatives of the leaders’ states and any other global information to be known by each follower. To reduce the effect on the varying gain during the adaption mainly caused by the initial error, fully distributed adaptive time-varying sliding-mode control is presented for controller design. To tackle the chattering effect caused by the discontinuous controller, we further propose a fully distributed continuous adaptive controller, under which both the containment errors and the adaptive gains are ultimately bounded. Simulation results are given to illustrate the theoretical results.
Keywords: Multiple Lagrangian system; Containment control; Distributed control; Sliding-mode control


Editorial Board,
Systems & Control Letters,
Volume 72,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00185-6.
(http://www.sciencedirect.com/science/article/pii/S0167691114001856)

Sei Zhen Khong, Michael Cantoni,
Gap metrics for time-varying linear systems in a continuous-time setting,
Systems & Control Letters,
Volume 70,
2014,
Pages 118-126,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114001339)
Abstract: A recently proposed time-varying generalisation of Vinnicombe’s ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.
Keywords: Feedback; Linear time-varying systems; Robust stability

Deqing Huang, Xuefang Li, Jian-Xin Xu, Chao Xu, Wei He,
Iterative learning control of inhomogeneous distributed parameter systems—frequency domain design and analysis,
Systems & Control Letters,
Volume 72,
2014,
Pages 22-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114001613)
Abstract: This paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems (LIDPSs), which may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the system model characteristics, LIDPSs are first reformulated into a matrix form in the Laplace transform domain. Then, through the determination of a fundamental matrix, the transfer function of LIDPS is precisely evaluated in a closed form. The derived transfer function provides the direct input–output relationship of the LIDPS, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and make full use of the process repetition, while avoid any simplification or discretization for the 3D dynamics of LIDPS in the time, space, and iteration domains. In the end, two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme.
Keywords: Iterative learning control; Inhomogeneous distributed parameter system; Transfer function; Boundary control

Shaikshavali Chitraganti, Samir Aberkane, Christophe Aubrun, Guillermo Valencia-Palomo, Vasile Dragan,
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach,
Systems & Control Letters,
Volume 74,
2014,
Pages 81-89,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114002308)
Abstract: In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.
Keywords: Jump linear systems; Stochastic model predictive control; Probabilistic state constraints; Linear state-feedback; Second moment stability

Bin Zhang, Yingmin Jia, Fumitoshi Matsuno,
Finite-time observers for multi-agent systems without velocity measurements and with input saturations,
Systems & Control Letters,
Volume 68,
2014,
Pages 86-94,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114000802)
Abstract: This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.
Keywords: Finite-time observers; Multi-agent systems; Distributed protocols; Input saturations

Thomas Berger, Stephan Trenn,
Kalman controllability decompositions for differential-algebraic systems,
Systems & Control Letters,
Volume 71,
2014,
Pages 54-61,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114001340)
Abstract: We study linear differential-algebraic control systems and investigate decompositions with respect to controllability properties. We show that the augmented Wong sequences can be exploited for a transformation of the system into a Kalman controllability decomposition (KCD). The KCD decouples the system into a completely controllable part, an uncontrollable part given by an ordinary differential equation and an inconsistent part, which is behaviorally controllable but contains no completely controllable part. This decomposition improves a known KCD from a behavioral point of view. We conclude the paper with some features of the KCD in the case of regular systems.
Keywords: Differential-algebraic systems; Descriptor systems; Controllability; Kalman decomposition; Wong sequences

Huaiqiang Yu,
Equivalence of minimal time and minimal norm control problems for semilinear heat equations,
Systems & Control Letters,
Volume 73,
2014,
Pages 17-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114002035)
Abstract: In this paper, we establish the equivalence of minimal time and minimal norm control problems for semilinear heat equations in which the controls are distributed internally in an open subset of the state domain. As an application, the Bang–Bang property for minimal norm controls are also presented.
Keywords: Minimal time control; Minimal norm control; Bang–Bang property; Semilinear heat equation

Joris Bierkens, Hilbert J. Kappen,
Explicit solution of relative entropy weighted control,
Systems & Control Letters,
Volume 72,
2014,
Pages 36-43,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114001583)
Abstract: We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete characterization of the situations in which a finite optimal value exists and the situations in which a minimizing probability distribution exists. Specializing to the case where the underlying probability distribution is Wiener measure, we characterize finite relative entropy changes of measure in terms of square integrability of the corresponding change of drift. For the optimal change of measure for the relative entropy weighted optimization, an expression involving the Malliavin derivative of the cost random variable is derived. The theory is illustrated by its application to several examples, including the case where the cost variable is the maximum of a standard Brownian motion over a finite time horizon. For this example we obtain an exact optimal drift, as well as an approximation of the optimal drift through a Monte-Carlo algorithm.
Keywords: Stochastic optimal control; Itô calculus; Brownian motion; Malliavin calculus; Relative entropy; Path integral control; Monte-Carlo sampling

Chang Duan, Fen Wu,
Analysis and control of switched linear systems via dwell-time min-switching,
Systems & Control Letters,
Volume 70,
2014,
Pages 8-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114001066)
Abstract: This paper addresses analysis and switching control problems of switched linear systems. To this end, a mixed time-driven and state-dependent switching strategy is proposed. It guarantees an average dwell time even when all subsystems are unstable. The switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and satisfy a weighted L2 gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min-switching based designs. The effectiveness of the proposed approach has been illustrated through a spherical inverted pendulum example.
Keywords: Switched linear system; Dwell-time; Min-switching; Bilinear matrix inequality; Stabilization and weighted L2 gain

W. Steven Gray, Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard,
Faà di Bruno Hopf algebra of the output feedback group for multivariable Fliess operators,
Systems & Control Letters,
Volume 74,
2014,
Pages 64-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114002278)
Abstract: Given two nonlinear input–output systems written in terms of Chen–Fliess functional expansions, i.e., Fliess operators, it is known that the feedback interconnected system is always well defined and in the same class. An explicit formula for the generating series of a single-input, single-output closed-loop system was provided by the first two authors in earlier work via Hopf algebra methods. This paper is a sequel. It has four main innovations. First, the full multivariable extension of the theory is presented. Next, a major simplification of the basic setup is introduced using a new type of grading that has recently appeared in the literature. This grading also facilitates a fully recursive algorithm to compute the antipode of the Hopf algebra of the output feedback group, and thus, the corresponding feedback product can be computed much more efficiently. The final innovation is an improved convergence analysis of the antipode operation, namely, the radius of convergence of the antipode is computed.
Keywords: Formal power series; Functional series; Hopf algebras; Output feedback; Nonlinear systems

A.H. González, A. Ferramosca, G.A. Bustos, J.L. Marchetti, M. Fiacchini, D. Odloak,
Model predictive control suitable for closed-loop re-identification,
Systems & Control Letters,
Volume 69,
2014,
Pages 23-33,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114000772)
Abstract: The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification, a persistent excitation of the system is needed, while the control objective is to stabilize the system at a given equilibrium point. However, a generalization of the concept of stability, from punctual stability to (invariant) set stability, allows for a flexibility that can be used to avoid the conflict between these objectives. Taking into account that an invariant target set includes not only a stationary component, but also a transient one, the system could be excited without deteriorating the stability of the closed-loop. In this work, a MPC controller is proposed that ensures the stability of invariant sets at the same time that a signal suitable for closed-loop re-identification is generated. Several simulation results show the propose controller formulation properties.
Keywords: Model predictive control; Closed-loop identification; Target set control; Persistent excitation

Xin Yu, Chao Xu, Jian Chu,
Local exponential stabilization of Fisher’s equation using the backstepping technique,
Systems & Control Letters,
Volume 74,
2014,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114001984)
Abstract: This paper deals with the boundary stabilization problem for the 1D Fisher’s partial differential equation (PDE) defined on a bounded interval, which is a nonlinear unstable distributed parameter system. The stabilizing controller derived using the backstepping technique for linear parabolic PDEs (associated with Fisher’s PDE) can be extended to the nonlinear case. In the work, we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed-loop nonlinear Fisher’s system exponentially stable (with any desired decay rate) locally in both L2(0,1) and H1(0,1), respectively. The effectiveness of the control synthesis approach is illustrated by a numerical simulation.
Keywords: Backstepping; Local stabilization; Boundary feedback; Fisher’s equation

Xinghu Wang, Dabo Xu, Yiguang Hong,
Consensus control of nonlinear leader–follower multi-agent systems with actuating disturbances,
Systems & Control Letters,
Volume 73,
2014,
Pages 58-66,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.004.
(http://www.sciencedirect.com/science/article/pii/S016769111400200X)
Abstract: This paper studies a semi-global asymptotic consensus problem of nonlinear multi-agent systems with local actuating disturbances. For a modest nonlinear scenario, a consensus protocol is proposed based on a viable two-layer network. The consensus problem is treated as distributed output regulation, which is resolved by a joint decomposition of the zero-error constraint inputs and a configuration of a flexible internal model network. An illustrative example is also given to show the efficiency of the two-layer networked design.
Keywords: Multi-agent systems; Disturbances; Distributed control; Networked control

Haitao Li, Yuzhen Wang, Lihua Xie, Daizhan Cheng,
Disturbance decoupling control design for switched Boolean control networks,
Systems & Control Letters,
Volume 72,
2014,
Pages 1-6,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114001601)
Abstract: This paper investigates a kind of disturbance decoupling problems (DDPs) for switched Boolean control networks (BCNs), that is, the disturbance-independent output decoupling problem, via the semi-tensor product of matrices. By converting the dynamics of switched BCNs into an algebraic form and using the redundant variable separation technique, all possible state feedback controllers are designed for the disturbance-independent output decoupling problem. Then, based on the obtained state feedback disturbance decoupling controllers and the system’s output equation, a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers. The study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched BCNs.
Keywords: Switched Boolean control network; Disturbance decoupling; Control design; Semi-tensor product of matrices

Junmin Peng, Xudong Ye,
Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs,
Systems & Control Letters,
Volume 68,
2014,
Pages 51-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114000632)
Abstract: In this paper, we investigate the cooperative control of networked agents with unknown high-frequency-gain signs. A Nussbaum-type adaptive controller is designed for each agent such that consensus of the network can be achieved while all signals in the overall system maintain bounded. The distributed controller for each agent has two parts: neighborhood error between itself and the neighbors and a Nussbaum-type item for seeking control direction adaptively. The argument of the Nussbaum-type function is tuned on line via an appropriately designed update law. It is proved that when the undirected graph is connected or the balanced digraph is weakly connected, consensus of the network can be realized. Furthermore, a distributed asymptotic regulator is proposed to regulate the overall system to the equilibrium. Simulation results are presented to verify the effectiveness of the proposed controllers.
Keywords: Consensus; Distributed; Nussbaum; Adaptive; Unknown high-frequency-gain

Chong-Jin Ong, Zheming Wang,
Reducing variables in Model Predictive Control of linear system with disturbances using singular value decomposition,
Systems & Control Letters,
Volume 71,
2014,
Pages 62-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114001327)
Abstract: Arising from the need to reduce online computations of Model Predictive Controller, this paper proposes an approach for a linear system with bounded additive disturbance using fewer variables than the standard. The new variables are chosen so that they transfer the maximal energy to the control inputs. Several other features are introduced. These include an auxiliary state to ensure recursive feasibility, an initialization procedure that recovers a substantial portion of the original domain of attraction arising from the use of fewer variables. A comparison of the domains of attraction associated with the new variables is also discussed. Run-time computational advantage of more than an order of magnitude compared with standard approach is demonstrated using several numerical examples although a more expensive initialization is needed.
Keywords: Model Predictive Control; Reduced number of variables; Domain of attraction

F. Cacace, A. Germani, C. Manes,
Exponential stabilization of linear systems with time-varying delayed state feedback via partial spectrum assignment,
Systems & Control Letters,
Volume 69,
2014,
Pages 47-52,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.007.
(http://www.sciencedirect.com/science/article/pii/S016769111400098X)
Abstract: We consider the problem of controlling a linear system when the state is available with a known time-varying delay (delayed-state feedback control) or the actuator is affected by a delay. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system to guarantee the exponential zero-state stability with a prescribed decay rate by means of a finite-dimensional control law. A non conservative bound on the maximum allowed delay for the prescribed decay rate is presented, which holds for both cases of constant and time-varying delays. An advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required. We compare the performance of our approach, in terms of delay bound and input signal, with another recent approach.
Keywords: Feedback stabilization; Delay compensation; Linear time-delay systems

Ridong Zhang, Furong Gao,
An improved decoupling structure based state space MPC design with improved performance,
Systems & Control Letters,
Volume 75,
2015,
Pages 77-83,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114002539)
Abstract: In this paper, an improved decoupling structure is first proposed for multivariable processes, where the resulted decoupler can avoid zero-pole cancelation and simultaneously guarantee feasibility by tuning of additional parameters. A subsequent single-input–single-output design of model predictive control (MPC) is then proposed using a new state space realization of the independent single loops, where we adopt a new extended non-minimal state space structure to enhance control performance. Through this new design model, dynamics of processes’ state variables can be directly taken into account. The decoupler property, closed-loop control performance, the relationship with traditional state space MPC and robust stability issues are fully analyzed. The efficiency of the proposed is evaluated through a typical process in the recent literature, in comparison with a typical non-minimal state space MPC recently developed.
Keywords: Model predictive control; State space model; Closed-loop control performance; Discrete time processes

Masashi Wakaiki, Yutaka Yamamoto,
Stable controller design for mixed sensitivity reduction of infinite-dimensional systems,
Systems & Control Letters,
Volume 72,
2014,
Pages 80-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114001571)
Abstract: In this paper we study the design of stable controllers for mixed sensitivity reduction for systems that have input/output delays and infinitely many unstable zeros. The proposed method is based on interpolation with a unit in H∞, which gives a necessary and sufficient condition for stabilization by stable controllers. Using the Youla parameterization, we introduce a two-block problem for the stable H∞ controller design. The two-block problem is then transformed to a one-block problem solvable by the skew Toeplitz approach.
Keywords: Strong stabilization; Infinite-dimensional systems; H∞ control

Robert Schmid, Lorenzo Ntogramatzidis,
Nonovershooting and nonundershooting exact output regulation,
Systems & Control Letters,
Volume 70,
2014,
Pages 30-37,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114001054)
Abstract: We consider the classic problem of exact output regulation for a linear time invariant plant. Under the assumption that either a state feedback or measurement feedback output regulator exists, we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response.
Keywords: Linear systems; Tracking control; Nonovershooting transient response

Luka Grubišić, Daniel Kressner,
On the eigenvalue decay of solutions to operator Lyapunov equations,
Systems & Control Letters,
Volume 73,
2014,
Pages 42-47,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114002023)
Abstract: This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in k, provided that the involved operator A generates an exponentially stable analytic semigroup, and A is either self-adjoint or diagonalizable with its eigenvalues contained in a strip around the real axis. Numerical experiments with discretizations of 1D and 2D PDE control problems confirm this decay.
Keywords: Balanced truncation; Exponential decay; Lyapunov equation

Márcio J. Lacerda, Sophie Tarbouriech, Germain Garcia, Pedro L.D. Peres,
ℋ∞ filter design for nonlinear polynomial systems,
Systems & Control Letters,
Volume 70,
2014,
Pages 77-84,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.014.
(http://www.sciencedirect.com/science/article/pii/S0167691114001297)
Abstract: The problem of ℋ∞ filter design for continuous-time nonlinear polynomial systems is addressed in this paper. The aim is to design a full order dynamic filter that depends polynomially on the filter states. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an ℋ∞ performance bound for the augmented polynomial system, composed by the original system and the filter to be designed, in a regional (local) context. Then, by using Finsler’s lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices in the conditions. Imposing structural constraints to the decision variables and fixing some values for a scalar parameter, design conditions for the ℋ∞ filter can be obtained in terms of linear matrix inequalities. As illustrated by numerical experiments, the proposed conditions can improve the ℋ∞ performance provided by standard linear filtering by including the polynomial terms in the filter dynamics.
Keywords: Polynomial systems; ℋ∞ filtering; Linear matrix inequalities

Enrique Fernández-Cara, Mauricio C. Santos,
Numerical null controllability of the 1D linear Schrödinger equation,
Systems & Control Letters,
Volume 73,
2014,
Pages 33-41,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.017.
(http://www.sciencedirect.com/science/article/pii/S0167691114001972)
Abstract: This paper deals with the numerical approximation to boundary controls that drive the solution to the 1D linear Schrödinger equation to a prescribed state at a final time. Using ideas from Fursikov and Imanuvilov, we consider the control that minimizes over the class of admissible controls a functional that involves weighted integrals, with weights that blow up at  T. We will see that this extremal problem is equivalent to a differential problem that is fourth order in space and second order in time. Adapting some numerical techniques applied by the first author and Münch to the heat equation, we approximate the variational formulation by introducing appropriate space–time finite elements that are C1 in space and C0 in time. We present two approaches; the second one relies on a change of variable which leads to a lower condition number for the stiffness matrix. The results of some experiments show the efficiency of these methods.
Keywords: 1D Schrödinger equation; Exact controllability; Finite element methods; Carleman inequalities


Editorial Board,
Systems & Control Letters,
Volume 69,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00117-0.
(http://www.sciencedirect.com/science/article/pii/S0167691114001170)

Chaoyong Li, Zhihua Qu, Mary Ann Weitnauer,
Distributed extremum seeking and formation control for nonholonomic mobile network,
Systems & Control Letters,
Volume 75,
2015,
Pages 27-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114002382)
Abstract: In this paper, an integrated control and optimization problem is studied in the context of formation and coverage of a cluster of nonholonomic mobile robots. In particular, each communication channel is modeled by its outage probability, and hence, connectivity is maintained if the outage probability is less than a certain threshold. The objective of the communication network is to not only maintain resilient communication quality but also extend the network coverage. An information theory based performance index is defined to quantify this control objective. Unlike most of the existing results, the proposed cooperative control design does not assume the knowledge of any gradient (of the performance index). Rather, a distributed extremum seeking algorithm is designed to optimize the connectivity and coverage of the mobile network. The proposed approach retains all the advantages of cooperative control, and it can not only perform extremum seeking individually, but also ensures a consensus of estimates between any pair of connected systems. Simulation results demonstrate effectiveness of the proposed methodology.
Keywords: Formation control; Extremum seeking; Nonholonomic vehicle

Nikolaos Bekiaris-Liberis,
Simultaneous compensation of input and state delays for nonlinear systems,
Systems & Control Letters,
Volume 73,
2014,
Pages 96-102,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.014.
(http://www.sciencedirect.com/science/article/pii/S0167691114001832)
Abstract: The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.
Keywords: Delay systems; Nonlinear systems; Predictor feedback

Rui-Juan Liu, Guo-Ping Liu, Min Wu, Jinhua She, Zhuo-Yun Nie,
Robust disturbance rejection in modified repetitive control system,
Systems & Control Letters,
Volume 70,
2014,
Pages 100-108,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.06.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114001315)
Abstract: This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.
Keywords: Aperiodic disturbance; Disturbance rejection; Equivalent input disturbance (EID); Linear matrix inequality (LMI); Repetitive control; Robust control; State observer

Peter C. Young,
Comment on ‘Projection-based identification algorithm for grey-box continuous-time models’ by Ichiro Maruta and Toshiharu Sugie,
Systems & Control Letters,
Volume 69,
2014,
Pages 62-64,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114000863)
Abstract: Although the paper by Maruta and Sugie (2013) makes an interesting contribution to the literature on the estimation of parameters in grey-box, continuous-time transfer function models, some of the simulation results are flawed and give a misleading impression of how the algorithm suggested by the authors compares with the well known and closely related SRIVC algorithm.
Keywords: Parameter estimation; Continuous-time; Transfer function models; Refined instrumental variable algorithms

Shuli Sun, Guanghui Wang,
Modeling and estimation for networked systems with multiple random transmission delays and packet losses,
Systems & Control Letters,
Volume 73,
2014,
Pages 6-16,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114001558)
Abstract: In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.
Keywords: Optimal linear filter; Random transmission delay; Packet loss; Steady state; Orthogonal projection approach

Jovan Stefanovski,
Kalman–Yakubovič–Popov lemma for descriptor systems,
Systems & Control Letters,
Volume 74,
2014,
Pages 8-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.015.
(http://www.sciencedirect.com/science/article/pii/S0167691114001959)
Abstract: For a given descriptor realization of para-hermitian rational matrix Π(s), we present a generalization of Kalman–Yakubovič–Popov lemma, i.e. necessary and sufficient conditions for Π≥0 on the imaginary axis, in terms of an inequality with constant matrices. The result is quite general, since Π can have poles and zeros on the extended imaginary axis, hence the nonstrict inequality Π(jω)≥0, ω∈R can hold, instead of the strict inequality. Π can be singular. The descriptor realization is required to be only impulse controllable and controllable (or stabilizable and detΠ≠0). A spectral factorization of Π is given, by the above mentioned constant matrices. Three consequences of the generalized KYP lemma, and an illustrative numerical example are given.
Keywords: Kalman–Yakubovič–Popov lemma; Descriptor systems

Xiaotao Liu, Yang Shi, Daniela Constantinescu,
Distributed model predictive control of constrained weakly coupled nonlinear systems,
Systems & Control Letters,
Volume 74,
2014,
Pages 41-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114002011)
Abstract: This paper proposes a distributed model predictive control (MPC) strategy for a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances. In the proposed strategy, all subsystems compute their control signals by solving local optimizations constrained by their nominal decoupled dynamics. The dynamic couplings and the disturbances are accommodated through new robustness constraints in the local optimizations. The paper derives relationships among, and designs procedures for, the parameters involved in the proposed distributed MPC strategy based on the analysis of the recursive feasibility and the robust stability of the overall system. The paper shows that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. Moreover, it establishes sufficient conditions for the overall system state to converge to a robust positively invariant set. The paper illustrates the effectiveness of the proposed distributed MPC strategy by applying it to three coupled cart-(nonlinear) spring–damper subsystems.
Keywords: Distributed model predictive control (MPC); Coupled nonlinear system; Optimization; Recursive feasibility

G. Conte, A.M. Perdon, N. Otsuka,
The disturbance decoupling problem with stability for switching dynamical systems,
Systems & Control Letters,
Volume 70,
2014,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114001042)
Abstract: The disturbance decoupling problem with stability is dealt with by means of the geometric approach for switching systems. The existence of feedbacks which decouple the disturbance and, at the same time, assure stability is difficult to characterize, since the action of the feedback couples with that of the switching law. Under suitable conditions, it is shown that the above requirement can be dealt with in separate ways and this allows us to state a checkable necessary condition and, on that basis, also a sufficient condition for solvability of the problem.
Keywords: Switching systems; Disturbance decoupling; Geometric approach

Samuel Coogan, Murat Arcak,
A computational approach to synthesizing guards for hybrid systems,
Systems & Control Letters,
Volume 73,
2014,
Pages 25-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.016.
(http://www.sciencedirect.com/science/article/pii/S0167691114001960)
Abstract: We propose a technique for synthesizing switching guards for hybrid systems to satisfy a given state-based safety constraint. Using techniques from sum of squares (SOS) optimization, we design guards defined by semialgebraic sets that trigger mode switches, and we guarantee that the synthesized switching policy does not allow Zeno executions. We demonstrate our approach on an example of switched affine systems and on an application to traffic ramp metering.
Keywords: Hybrid systems; Guard synthesis; Computational methods

Innocent Okoloko, Yoonsoo Kim,
Attitude synchronization of multiple spacecraft with cone avoidance constraints,
Systems & Control Letters,
Volume 69,
2014,
Pages 73-79,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114000991)
Abstract: In this paper, we consider a team of spacecraft which requires changing its orientation to a common attitude using a decentralized control scheme under a connected communication topology, while satisfying cone avoidance constraints due to blind celestial objects, plume impingement and so on. For this purpose, we first combine consensus theory and optimization theory to develop a quaternion-based attitude consensus protocol. Based on the communication graph at each time step, each spacecraft generates a guidance command or reference attitude trajectory by synthesizing a series of Laplacian-like matrix P(t), using semidefinite programming (SDP) which involves linear matrix inequalities (LMIs). It is analytically shown that this series of matrices P(t) is capable of collectively driving the initial attitudes to a common consensus attitude. For satisfying cone avoidance constraints, exclusion zones are then identified and expressed as LMIs. This identification of the exclusion zones gives rise to selecting safe waypoints from the reference attitude trajectory and then to passing through the selected waypoints while avoiding the exclusion zones via proper control inputs. This solution procedure is demonstrated via numerical simulations of coordinated attitude rendezvous and attitude formation acquisition of multiple spacecraft with cone avoidance manoeuvres.
Keywords: Constrained attitude control; Cone avoidance; Attitude synchronization; Graph Laplacian; Cooperative distributed control


Editorial Board,
Systems & Control Letters,
Volume 70,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00139-X.
(http://www.sciencedirect.com/science/article/pii/S016769111400139X)

Lassi Paunonen,
Robustness of strong stability of discrete semigroups,
Systems & Control Letters,
Volume 75,
2015,
Pages 35-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.11.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114002370)
Abstract: In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded perturbations. As the main result we present classes of perturbations preserving the strong stability of the semigroup.
Keywords: Discrete semigroup; Strong stability; Robustness

Fatima Zohra Taousser, Michael Defoort, Mohamed Djemai,
Stability analysis of a class of switched linear systems on non-uniform time domains,
Systems & Control Letters,
Volume 74,
2014,
Pages 24-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.012.
(http://www.sciencedirect.com/science/article/pii/S0167691114002096)
Abstract: This paper deals with the stability analysis of a class of switched linear systems on non-uniform time domains. The considered class consists of a set of linear continuous-time and linear discrete-time subsystems. First, some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentially stable. These results are extended when considering an unstable discrete time subsystem or an unstable continuous-time subsystem. Some examples illustrate these results.
Keywords: Time scales; Switched systems; Stability analysis; Exponential stability

Guoxiang Gu, Li Qiu,
Networked control systems for multi-input plants based on polar logarithmic quantization,
Systems & Control Letters,
Volume 69,
2014,
Pages 16-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114000619)
Abstract: This paper investigates the use of polar logarithmic quantization (PLQ) for multi-input systems, and the corresponding design issues for the underlying networked control system (NCS). It is shown that the PLQ induces sector bounded nonlinear uncertainties in multiplicative and relative forms for vector-valued analog signals, similar to those in the scalar case. For the two-input NCS, optimal quantization is obtained through minimization of the quantization error that is quantified explicitly. The results are extended to more than two-input NCSs with an upper bound derived for the quantization error. Feedback stabilization and control of the NCS are also investigated under the PLQ at the plant input under state feedback. The coarsest quantization density (CQD) is studied and obtained. Results in this paper are illustrated by a numerical example.
Keywords: Quadratic stability; Quantization errors; Robust control

Jianqiang Hu, Jinde Cao, Jie Yu, Tasawar Hayat,
Consensus of nonlinear multi-agent systems with observer-based protocols,
Systems & Control Letters,
Volume 72,
2014,
Pages 71-79,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.07.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114001546)
Abstract: This paper is concerned with distributed pinning consensus problem for a class of nonlinear multi-agent system with observer-based protocols. Two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents. According to the state information observed, a distributed pinning observer-based protocol is proposed for the leader-following consensus of the multi-agent system. Furthermore, two multi-step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively. It is shown that under the condition that the pinning joint communication topology contains a directed spanning tree, the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable, but also guarantee the consensus of the multi-agent system to be solved asymptotically. Finally, two numerical examples are provided to demonstrate the effectiveness of the observer-based protocols.
Keywords: Pinning consensus; Nonlinear multi-agent system; Distributed pinning observer

Pierre Lissy,
An application of a conjecture due to Ervedoza and Zuazua concerning the observability of the heat equation in small time to a conjecture due to Coron and Guerrero concerning the uniform controllability of a convection–diffusion equation in the vanishing viscosity limit,
Systems & Control Letters,
Volume 69,
2014,
Pages 98-102,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114001029)
Abstract: The aim of this short paper is to explore a new connection between a conjecture concerning sharp boundary observability estimates for the 1-D heat equation in small time and a conjecture concerning the cost of null-controllability for a 1-D convection–diffusion equation with constant coefficients controlled on the boundary in the vanishing viscosity limit, in the spirit of what was done in Pierre Lissy (2012). We notably establish that the first conjecture implies the second one as soon as the speed of the transport part is non-negative in the transport-diffusion equation.
Keywords: Transport-diffusion equation; Null controllability; Vanishing viscosity limit

Mengtao Cao, Feng Xiao, Long Wang,
Second-order leader-following consensus based on time and event hybrid-driven control,
Systems & Control Letters,
Volume 74,
2014,
Pages 90-97,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.013.
(http://www.sciencedirect.com/science/article/pii/S0167691114001820)
Abstract: The leader-following consensus problem of multi-agent systems with double-integrator dynamics is considered in this paper. Herein, there is only one leader, the interaction topology among the followers is undirected, and the followers are reachable from the leader. A novel consensus protocol based on time and edge event hybrid-driven techniques is proposed, and two associated event-triggering rules are presented. Each edge event relies on the information of the corresponding two neighboring agents and event-triggering actions over different edges are independent of each other. It is shown that the proposed protocol can solve the leader-following consensus problem. Moreover, the controller-updating costs and communication costs are largely reduced. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.
Keywords: Multi-agent systems; Leader-following consensus; Edge events; Hybrid-driven control

Uwe Helmke, Michael Schönlein,
Uniform ensemble controllability for one-parameter families of time-invariant linear systems,
Systems & Control Letters,
Volume 71,
2014,
Pages 69-77,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.015.
(http://www.sciencedirect.com/science/article/pii/S0167691114001303)
Abstract: In this paper we derive necessary as well as sufficient conditions for approximate controllability of parameter-dependent linear systems in the supremum norm. Using tools from complex approximation theory, we prove the existence of parameter-independent open-loop controls that steer the zero initial state of an ensemble of linear systems uniformly to a prescribed family of terminal states. New necessary conditions for uniform ensemble controllability of single-input systems are derived. Our results extend earlier ones of Li for ensemble controllability of linear systems.
Keywords: Approximate controllability; Complex approximation; Ensemble controllability; Families of systems

Junjie Fu, Jinzhi Wang,
Adaptive coordinated tracking of multi-agent systems with quantized information,
Systems & Control Letters,
Volume 74,
2014,
Pages 115-125,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114001789)
Abstract: In this paper, we study the adaptive coordinated tracking problem for continuous-time first-order integrator systems with quantized information under switching undirected and fixed directed communication graphs, respectively. The combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated. Both the logarithmic quantizers and uniform quantizers are considered. It is shown that when logarithmic quantizers are used, exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used, practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter. Simulation examples are provided to illustrate the results.
Keywords: Multi-agent system; Coordinated tracking; Distributed observer; Directed graphs; Quantization effect

A. Gautam, Y.C. Soh,
Constraint-softening in model predictive control with off-line-optimized admissible sets for systems with additive and multiplicative disturbances,
Systems & Control Letters,
Volume 69,
2014,
Pages 65-72,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114000978)
Abstract: An approach to the softening of constraints is explored for a class of MPC algorithms that employ off-line-computed constraint-admissible sets for simplified on-line computations. The proposed approach relies on the use of exact penalty functions to ensure that the solution coincides with the actual optimal solution if the original MPC problem is feasible and that there are constraint violations at minimum possible levels if the original problem is infeasible. The approach is implemented for a class of linear systems with additive and multiplicative disturbances using a dynamic-policy-based MPC algorithm. Results specific to the cases of non-stochastic and stochastic disturbances are explored and assessed with simulation examples.
Keywords: Model predictive control (MPC); Soft-constrained MPC; Stochastic MPC; Feedback MPC; Additive and multiplicative disturbances

Mihai-Sorin Stupariu,
A quiver approach to studying orbit spaces of linear systems,
Systems & Control Letters,
Volume 73,
2014,
Pages 1-5,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.09.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114001947)
Abstract: Orbit spaces associated to linear actions are of particular interest in control theory. Their geometrical properties can be naturally investigated by using the representations of quivers as an abstract framework. The aim of the paper is to bring into attention an application of this approach and to show how the use of quivers makes it easy handling concepts arising in control theory. Specifically, the natural duality between controllable and observable systems, as well as the construction of compactifications for the associated orbit spaces is interpreted in terms of opposite quivers.
Keywords: Linear dynamical system; Quiver representation; Stability; Compactification

Majid Zamani, Alessandro Abate,
Approximately bisimilar symbolic models for randomly switched stochastic systems,
Systems & Control Letters,
Volume 69,
2014,
Pages 38-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.04.003.
(http://www.sciencedirect.com/science/article/pii/S016769111400084X)
Abstract: In the past few years there has been a growing interest in the use of symbolic models for control systems. The main reason is the possibility to leverage algorithmic techniques over symbolic models to synthesize controllers that are valid for the concrete control systems. Such controllers can enforce complex logical specifications that are otherwise hard (if not impossible) to establish on the concrete models with classical control techniques. Examples of such specifications include those expressible via linear temporal logic or as automata on infinite strings. A relevant goal in this research line is in the identification of classes of systems that admit symbolic models: in particular, continuous-time systems with stochastic or hybrid dynamics have been only recently considered, due to their rather general and complex dynamics. In this work we make progress in this direction by enlarging the class of stochastic hybrid systems admitting finite, symbolic models: specifically, we show that randomly switched stochastic systems, satisfying some incremental stability assumption, admit such models.
Keywords: Stochastic hybrid systems; Randomly switched models; Symbolic models; Finite abstractions; Formal synthesis

Li Li,
Coprime factor model reduction for discrete-time uncertain systems,
Systems & Control Letters,
Volume 74,
2014,
Pages 108-114,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.08.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114001790)
Abstract: This paper presents a contractive coprime factor model reduction approach for discrete-time uncertain systems of LFT form with norm bounded structured uncertainty. A systematic approach is proposed for coprime factorization and contractive coprime factorization of the underlying uncertain systems. The proposed coprime factor approach overcomes the robust stability restriction on the underlying systems which is required in the balanced truncation approach. Our method is based on the use of LMIs to construct the desired reduced dimension uncertain system model. Closed-loop robustness is discussed under additive coprime factor perturbations.
Keywords: Model reduction; Uncertain systems; Discrete-time systems; Coprime factorization


Editorial Board,
Systems & Control Letters,
Volume 75,
2015,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00259-X.
(http://www.sciencedirect.com/science/article/pii/S016769111400259X)


Editorial Board,
Systems & Control Letters,
Volume 74,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00240-0.
(http://www.sciencedirect.com/science/article/pii/S0167691114002400)

X. Cai, Y. Tan, S.Y. Li, I. Mareels,
On the finite time performance of model predictive control,
Systems & Control Letters,
Volume 70,
2014,
Pages 60-68,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.013.
(http://www.sciencedirect.com/science/article/pii/S0167691114001157)
Abstract: This paper addresses the finite time performance of model predictive control (MPC) for linear-time-invariant (LTI) systems without constraints. The performance of MPC is compared with that of finite horizon optimal control to find out how well model predictive control can perform relative to the optimal performance with the same or different horizons. By exploring the properties of the Riccati difference equation (RDE), an upper and a lower bound of the ratio between the finite time performance of MPC and finite horizon optimal cost are obtained. It is possible to extend the obtained results to more complicated systems such as nonlinear dynamic systems with constraints with appropriate generalizations. Simulation example supports our results.
Keywords: Model predictive control; Finite horizon optimal control; Riccati difference equation


Editorial Board,
Systems & Control Letters,
Volume 73,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00212-6.
(http://www.sciencedirect.com/science/article/pii/S0167691114002126)

Marcello Farina, Giulio Betti, Riccardo Scattolini,
Distributed predictive control of continuous-time systems,
Systems & Control Letters,
Volume 74,
2014,
Pages 32-40,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.10.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114002084)
Abstract: In the last years focus has been put in the development of distributed Model Predictive Control (MPC) algorithms. With a few exceptions, they have been mostly developed in the discrete-time framework. However, discretization of large-scale systems may destroy the sparsity of the original continuous-time models, making distributed control design and implementation more difficult. Also, more in general, discrete-time control of continuous-time systems does not allow to consider the process inter-sampling behavior. In this paper we present a novel non-cooperative distributed predictive control algorithm for continuous-time systems based on robust MPC concepts. The convergence properties of the proposed control scheme are stated, and its realizability is tested through a simulation case study.
Keywords: Distributed control; Continuous-time systems; Model predictive control; Robust control

V. Ugrinovskii, E. Fridman,
A Round-Robin type protocol for distributed estimation with H∞ consensus,
Systems & Control Letters,
Volume 69,
2014,
Pages 103-110,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.05.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114001030)
Abstract: The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a Round-Robin rule, at discrete time instances. The results of the paper are sufficient conditions which guarantee a suboptimal H∞ level of consensus between observers with sampled interconnections.
Keywords: Large-scale systems; Distributed estimation; Robust observers; Consensus; Vector dissipativity; Sampled-input systems; Time-delay systems

Qingling Wang, Changbin Yu, Huijun Gao,
Synchronization of identical linear dynamic systems subject to input saturation,
Systems & Control Letters,
Volume 64,
2014,
Pages 107-113,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.010.
(http://www.sciencedirect.com/science/article/pii/S0167691113002417)
Abstract: This paper investigates the synchronization problem for a group of agents with identical linear dynamics subject to input saturation. Two classes of linear systems, asymptotically null controllable with bounded control (ANCBC) systems and double-integrator systems, are studied. For ANCBC systems, it is shown that a linear protocol with the control gain obtained via parametric Lyapunov equations can semiglobally synchronize the undirected topology provided that its augmented directed topology has a spanning tree. For a special case of ANCBC, the double-integrator systems, it is established that if the augmented directed topology has a spanning tree, then in the presence of input saturation, using linear protocols with positive control gains can achieve global synchronization. Two numerical examples are given to demonstrate the effectiveness of the theoretical results.
Keywords: Identical linear dynamics; Input saturation; Multiagent systems; Synchronization

Tudor C. Ionescu, Alessandro Astolfi, Patrizio Colaneri,
Families of moment matching based, low order approximations for linear systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 47-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.011.
(http://www.sciencedirect.com/science/article/pii/S0167691113002338)
Abstract: The problem of finding a framework for linear moment matching based approximation of linear systems is discussed. It is shown that it is possible to define five (equivalent) notions of moments, i.e., one from a complex “s-domain” point of view, two using Krylov projections and two from a time-domain perspective. Based on these notions, classes of parameterized reduced order models that achieve moment matching are obtained. We analyze the controllability and observability properties of the models belonging to each of the classes of reduced order models. We find the subclasses of models of orders lower than the number of matched moments, i.e., we find the sets of parameters that allow for pole–zero cancellations to occur. Furthermore we compute the (subclass of) minimal order model(s). The minimal order is equal to half of the number of matched moments, i.e., generically the largest number of possible pole–zero cancellations is half of the number of matched moments. Finally, we present classes of reduced order models that match larger numbers of moments, based on interconnections between reduced order models.
Keywords: Moment matching; Family of reduced order models; Parameters; Pole–zero cancellation; Minimal; Interconnection

Y. Mo, E. Garone, B. Sinopoli,
On infinite-horizon sensor scheduling,
Systems & Control Letters,
Volume 67,
2014,
Pages 65-70,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114000401)
Abstract: In this paper we consider the problem of infinite-horizon sensor scheduling for estimation in linear Gaussian systems. Due to possible channel capacity, energy budget or topological constraints, it is assumed that at each time step only a subset of the available sensors can be selected to send their observations to the fusion center, where the state of the system is estimated by means of a Kalman filter. Several important properties of the infinite-horizon schedules will be presented in this paper. In particular, we prove that the infinite-horizon average estimation error and the boundedness of a schedule are independent of the initial covariance matrix. We further provide a constructive proof that any feasible schedule with finite average estimation error can be arbitrarily approximated by a bounded periodic schedule. We later generalized our result to lossy networks. These theoretical results provide valuable insights and guidelines for the design of computationally efficient sensor scheduling policies.
Keywords: Wireless sensor networks; Kalman filtering; Riccati equation

Alessandro Macchelli,
Dirac structures on Hilbert spaces and boundary control of distributed port-Hamiltonian systems,
Systems & Control Letters,
Volume 68,
2014,
Pages 43-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114000644)
Abstract: Aim of this paper is to show how the Dirac structure properties can be exploited in the development of energy-based boundary control laws for distributed port-Hamiltonian systems. Usually, stabilization of non-zero equilibria has been achieved by looking at, or generating, a set of structural invariants, namely Casimir functions, in closed-loop. Since this approach fails when an infinite amount of energy is required at the equilibrium (dissipation obstacle), this paper illustrates a novel approach that enlarges the class of stabilizing controllers. The starting point is the parametrization of the dynamics provided by the image representation of the Dirac structure, that is able to show the effects of the boundary inputs on the state evolution. In this way, energy-balancing and control by state-modulated source methodologies are extended to the distributed parameter scenario, and a geometric interpretation of these control techniques is provided. The theoretical results are discussed with the help of a simple but illustrative example, i.e. a transmission line with an RLC load in both serial and parallel configurations. In the latter case, energy-balancing controllers are not able to stabilize non-zero equilibria because of the dissipation obstacle. The problem is solved thanks to a (boundary) state-modulated source.
Keywords: Distributed port-Hamiltonian systems; Passivity-based boundary control; Dirac structures; Dissipation obstacle; Stability analysis

Edward N. Hartley, Jan M. Maciejowski,
Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints,
Systems & Control Letters,
Volume 66,
2014,
Pages 8-15,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114000127)
Abstract: A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.
Keywords: Model predictive control; Reconfigurable control; Fault-tolerant control


Editorial Board,
Systems & Control Letters,
Volume 68,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00088-7.
(http://www.sciencedirect.com/science/article/pii/S0167691114000887)


Editorial Board,
Systems & Control Letters,
Volume 67,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00067-X.
(http://www.sciencedirect.com/science/article/pii/S016769111400067X)

Yuan Liu, Haibo Min, Shicheng Wang, Zhiguo Liu, Shouyi Liao,
Distributed adaptive consensus for multiple mechanical systems with switching topologies and time-varying delay,
Systems & Control Letters,
Volume 64,
2014,
Pages 119-126,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.09.005.
(http://www.sciencedirect.com/science/article/pii/S0167691113001928)
Abstract: This paper studies the adaptive consensus problem of networked mechanical systems with time-varying delay and jointly-connected topologies. Two different consensus protocols are proposed. First, we present an adaptive consensus protocol for the connected switching topologies. Based on graph theory, Lyapunov stability theory and switching control theory, the stability of the proposed algorithm is demonstrated. Then we investigate the problem under the more general jointly-connected topologies, and with concurrent time-varying communication delay. The proposed consensus protocol consists of two parts: one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past. A distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters, time-varying delay and switching topologies in a unified theoretical framework. Numerical simulation is provided to demonstrate the effectiveness of the obtained results.
Keywords: Mechanical systems; Euler–Lagrange systems; Coordination control; Switching topologies; Parametric uncertainties; Time-varying delay

Peter Benner, Tobias Breiten,
On optimality of approximate low rank solutions of large-scale matrix equations,
Systems & Control Letters,
Volume 67,
2014,
Pages 55-64,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114000449)
Abstract: In this paper, we discuss some optimality results for the approximation of large-scale matrix equations. In particular, this includes the special case of Lyapunov and Sylvester equations, respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover, we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples, we show the efficiency of the proposed methods.
Keywords: Matrix equations; Low rank approximations; Rational Krylov subspaces; H2-model reduction

Hao Lu, Michael Di Loreto, Damien Eberard, Jean-Pierre Simon,
Approximation of distributed delays,
Systems & Control Letters,
Volume 66,
2014,
Pages 16-21,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114000097)
Abstract: In this paper, we address the approximation problem of distributed delays. These elements are convolution operators with kernel having bounded support and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and working on the convolution Banach algebra, a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control for time-delay systems.
Keywords: Distributed delay; Time-delay system; Rational; Approximation; Lumped system; Frequency analysis; Numerical implementation; Stabilization

Lijun Zhu, Zhiyong Chen,
Corrigendum to “Robust homogenization and consensus of nonlinear multi-agent systems” [Systems Control Lett. 65 (2014) 50–55],
Systems & Control Letters,
Volume 67,
2014,
Page 71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114000450)

Nguyen Huu Du, Nguyen Hai Dang, Nguyen Thanh Dieu,
On stability in distribution of stochastic differential delay equations with Markovian switching,
Systems & Control Letters,
Volume 65,
2014,
Pages 43-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.006.
(http://www.sciencedirect.com/science/article/pii/S0167691113002582)
Abstract: This paper provides a new sufficient condition for stability in distribution of stochastic differential delay equations with Markovian switching (SDDEs). It can be considered as an improvement to the result given by Yuan C. et al. in [6].
Keywords: Stochastic differential delay equations; Stability in distribution; Itô’s formula; Markov switching

Jing Na, Xuemei Ren, Yuanqing Xia,
Adaptive parameter identification of linear SISO systems with unknown time-delay,
Systems & Control Letters,
Volume 66,
2014,
Pages 43-50,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.005.
(http://www.sciencedirect.com/science/article/pii/S0167691114000255)
Abstract: An adaptive online parameter identification is proposed for linear single-input-single-output (SISO) time-delay systems to simultaneously estimate the unknown time-delay and other parameters. After representing the system as a parameterized form, a novel adaptive law is developed, which is driven by appropriate parameter estimation error information. Consequently, the identification error convergence can be proved under the conventional persistent excitation (PE) condition, which can be online tested in this paper. A finite-time (FT) identification scheme is further studied by incorporating the sliding mode scheme into the adaptation to achieve FT error convergence. The previously imposed constraint on the system relative degree is removed and the derivatives of the input and output are not required. Comparative simulation examples are provided to demonstrate the validity and efficacy of the proposed algorithms.
Keywords: System identification; Parameter estimation; Time-delay systems

Daniel E. Miller, Edward J. Davison,
Linear periodic controller design for decentralized control systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 1-11,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.007.
(http://www.sciencedirect.com/science/article/pii/S016769111300217X)
Abstract: In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.
Keywords: Decentralized control; Decentralized fixed modes; Quotient decentralized fixed modes; Linear periodic control

Shuxiang Guo,
Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 27-35,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.007.
(http://www.sciencedirect.com/science/article/pii/S0167691113002387)
Abstract: The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.
Keywords: Robust control; Guaranteed cost control; Non-fragile control; Robust reliability; Linear matrix inequality

Michael A. Demetriou,
Spatial PID consensus controllers for distributed filters of distributed parameter systems,
Systems & Control Letters,
Volume 63,
2014,
Pages 57-62,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.006.
(http://www.sciencedirect.com/science/article/pii/S0167691113002144)
Abstract: This paper considers the spatial penalization of the pairwise state estimate differences as used to enforce consensus in spatially distributed filters. A spatially distributed process, described by a parabolic partial differential equation is assumed to have a network of in-domain sensors. Each spatially distributed filter corresponds to a single sensor in the network and the goal is for these filters to collaboratively reach a consensus on the process state estimate. To enhance the agreement of the spatially distributed filters, the spatial gradient of the pairwise difference of state estimates is used as a means to penalize their disagreement. Additionally, a proportional and an integral penalization of the pairwise differences are also examined in order to produce a spatial proportional–integral–derivative penalization. To address the partial connectivity, certain conditions on the communication topology are given implicitly in terms of the inner product of the state estimation errors and their pairwise differences. Simulation studies provide an insight on the effects of this spatial penalizations.
Keywords: Distributed parameter systems; Spatially distributed filters; Spatial PID controllers; Consensus filters

Chris Guiver, Dave Hodgson, Stuart Townley,
Positive state controllability of positive linear systems,
Systems & Control Letters,
Volume 65,
2014,
Pages 23-29,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.002.
(http://www.sciencedirect.com/science/article/pii/S0167691113002545)
Abstract: Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inputs is often overly restrictive. Relaxing this requirement, the notion of positive state controllability of positive systems is introduced. A connection between positive state controllability and positive input controllability of a related system is established and used to obtain Kalman-like controllability criteria. In doing so we aim to encourage further study in this underdeveloped area.
Keywords: Controllability; Linear system; Discrete time; Positive system; Constrained system; Population ecology

Nikos Vlassis, Raphaël Jungers,
Polytopic uncertainty for linear systems: New and old complexity results,
Systems & Control Letters,
Volume 67,
2014,
Pages 9-13,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114000292)
Abstract: We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from control theory to systems engineering to biology. We focus on the algorithmic decidability of this property when one is given a particular polytope. This setting gives rise to several different algorithmic questions, depending on the nature of time (discrete/continuous), the property asked (stability/stabilizability), or the type of uncertainty (fixed/switching). Several of these questions have been answered in the literature in the last thirty years. We point out the ones that have remained open, and we answer all of them, except one which we raise as an open question. In all the cases, the results are negative in the sense that the questions are NP-hard. As a byproduct, we obtain complexity results for several other matrix problems in systems and control.
Keywords: Linear system; Polytopic uncertainty; Stability; Stabilizability; Computational complexity; NP-hardness

Yongqiang Li, Zhongsheng Hou,
Data-driven asymptotic stabilization for discrete-time nonlinear systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 79-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.003.
(http://www.sciencedirect.com/science/article/pii/S0167691113002302)
Abstract: In this paper, we propose a data-driven feedback controller design method based on Lyapunov approach, which can guarantee the asymptotic stability of the closed-loop and enlarge the estimate of domain of attraction (DOA) for the closed-loop. First, sufficient conditions for a feedback controller asymptotically stabilizing the discrete-time nonlinear plant are proposed. That is, if a feedback controller belongs to an open set consisting of pairs of control input and state, whose elements can make the difference of a control Lyapunov function (CLF) to be negative-definite, then the controller asymptotically stabilizes the plant. Then, for a given CLF candidate, an algorithm, to estimate the open set only using data, is proposed. With the estimate, it is checked whether the candidate is or is not a CLF. If it is, a feedback controller is designed just using data, which satisfies sufficient conditions mentioned above. Finally, the estimate of DOA for closed-loop is enlarged by finding an appropriate CLF from a CLF candidate set based on data. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided.
Keywords: Control Lyapunov function; Domain of attraction; Data-driven control; Stabilization; Nonlinear; Discrete-time

Q. Song, Y.D. Song,
Generalized PI control design for a class of unknown nonaffine systems with sensor and actuator faults,
Systems & Control Letters,
Volume 64,
2014,
Pages 86-95,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.011.
(http://www.sciencedirect.com/science/article/pii/S0167691113002429)
Abstract: This work deals with the tracking control problem of a class of unknown nonaffine dynamic systems that involve unpredictable sensor and actuation failures. As the control inputs enter into and influence the dynamic behavior of the nonaffine system through a nonlinear and implicit way, control design for such system becomes quite challenging. The underlying problem becomes even more complex if the system dynamics are unavailable for control design yet involving unanticipated sensor and/or actuator faults. In this work, a structurally simple and computationally inexpensive control scheme is proposed to achieve uniformly ultimately bounded (UUB) stable tracking control of a class of nonaffine systems. The proposed control is of a generalized PI form and is able to accommodate both sensor and actuator faults. The effectiveness of the proposed control strategy is confirmed by theoretical analysis and numerical simulations.
Keywords: Nonaffine systems; Sensor failures; Actuator failures; Generalized control; Fault-tolerant; Lipschitz condition

Zhicheng Li, Huijun Gao, Hamid Reza Karimi,
Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay,
Systems & Control Letters,
Volume 66,
2014,
Pages 85-93,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.010.
(http://www.sciencedirect.com/science/article/pii/S0167691113002624)
Abstract: This paper studies the problems of stability analysis and H∞ controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of the system based on the direct Lyapunov method in another perspective. The proposed stability condition is demonstrated to be less conservative than most existing results. Moreover, an admissible controller, which solves the problem of H∞ controller synthesis, is formulated into a convex optimization problem. Illustrative examples are provided to show the advantage and the effectiveness of the proposed method.
Keywords: H∞ control synthesis; Scaled small gain theorem; Stability analysis; Switched systems; Time-delay systems

Antonio Barreiro, Alfonso Baños, Sebastián Dormido, José A. González-Prieto,
Reset control systems with reset band: Well-posedness, limit cycles and stability analysis,
Systems & Control Letters,
Volume 63,
2014,
Pages 1-11,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.002.
(http://www.sciencedirect.com/science/article/pii/S0167691113002107)
Abstract: Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed, for example, the anticipation of the reset condition with the so-called reset band. There is a lack of analysis tools for reset systems with reset band. In this paper we address this problem by means of Poincaré maps (PM). It is shown how PM can predict the existence and stability of limit cycles, and give also information on pathologies such as Zenoness, and provide parameter ranges where the system is guarded against those behaviors and thus global asymptotical stability (GAS) is guaranteed.
Keywords: Reset control; Poincaré maps; Limit cycles; Zeno solutions

Junfeng Zhang, Zhengzhi Han, Fubo Zhu, Xudong Zhao,
Absolute exponential stability and stabilization of switched nonlinear systems,
Systems & Control Letters,
Volume 66,
2014,
Pages 51-57,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.021.
(http://www.sciencedirect.com/science/article/pii/S0167691114000115)
Abstract: This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.
Keywords: Absolute exponential stability; Switched nonlinear systems; Multiple Lyapunov functions; Average dwell time switching

Daniel Petersson, Johan Löfberg,
Model reduction using a frequency-limited H2-cost,
Systems & Control Letters,
Volume 67,
2014,
Pages 32-39,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114000437)
Abstract: We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited H2 like cost function. An important contribution of the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem.
Keywords: Model reduction; H2-norm; Optimization

Jiandong Zhu,
Stabilization and synchronization for a heterogeneous multi-agent system via harmonic control,
Systems & Control Letters,
Volume 66,
2014,
Pages 1-7,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.019.
(http://www.sciencedirect.com/science/article/pii/S0167691114000085)
Abstract: In this paper, a class of heterogeneous multi-agent systems with directed cycle graphs is investigated. The stabilization and synchronization problems via harmonic control are solved under some conditions and the feedback control gains are constructively designed. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.
Keywords: Heterogeneous multi-agent systems; Stabilization; Synchronization; Harmonic control; Cycle graph

Guilherme Mazanti,
Stabilization of persistently excited linear systems by delayed feedback laws,
Systems & Control Letters,
Volume 68,
2014,
Pages 57-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114000760)
Abstract: This paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback is indeed possible, generalizing a previous result already known for non-delayed feedback laws.
Keywords: Stabilization; Switched systems; Persistent excitation; Delayed feedback

Jianshu Li, Yuanjin Zheng, Zhiping Lin,
Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms,
Systems & Control Letters,
Volume 66,
2014,
Pages 104-110,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.004.
(http://www.sciencedirect.com/science/article/pii/S0167691114000243)
Abstract: In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.
Keywords: Recursive identification; Time-varying system; Self-tuning; RLS algorithm; Matrix forgetting factor RLS algorithm

D.C. Tarraf, D. Bauso,
Finite alphabet control of logistic networks with discrete uncertainty,
Systems & Control Letters,
Volume 64,
2014,
Pages 20-26,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.013.
(http://www.sciencedirect.com/science/article/pii/S0167691113002351)
Abstract: We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples.
Keywords: Finite alphabets; Logistic networks; Control invariance; Discrete disturbances; Robustness


Editorial Board,
Systems & Control Letters,
Volume 66,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00048-6.
(http://www.sciencedirect.com/science/article/pii/S0167691114000486)


Editorial Board,
Systems & Control Letters,
Volume 65,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00032-2.
(http://www.sciencedirect.com/science/article/pii/S0167691114000322)

Xu Zhang, Yan Lin,
Global stabilization of high-order nonlinear time-delay systems by state feedback,
Systems & Control Letters,
Volume 65,
2014,
Pages 89-95,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.015.
(http://www.sciencedirect.com/science/article/pii/S0167691114000048)
Abstract: We consider the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-delay. By developing a novel dynamic gain-based backstepping approach, a state feedback controller independent of the time-delay is explicitly constructed with the help of appropriate Lyapunov–Krasovskii functionals. The precise knowledge (even the upper bound) of the time-delay is not required. It is proved that the states of the nonlinear time-delay systems can be regulated to the origin while all the closed loop signals are globally bounded. Finally, both physical and academic examples are given to illustrate the applications of the proposed scheme.
Keywords: High-order nonlinear systems; Time-delay; State feedback; Dynamic gain-based backstepping

Prathyush P. Menon, Christopher Edwards, Ian Postlethwaite,
L2 optimal decentralised static output feedback stabilisation of a network of dynamical systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 64-71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.008.
(http://www.sciencedirect.com/science/article/pii/S0167691113002399)
Abstract: In this paper global L2  stabilisation of a network of dynamical systems is attained by local decentralised static output feedback control. The proposed synthesis procedure guarantees an upper bound on the achievable L2  performance in the presence of disturbances. The synthesis of such a controller is posed as an iterative LMI optimisation problem. The algorithm is guaranteed to achieve a local minimum as a result of the iterations. The synthesis of the controller is independent of the number of nodes in the network and depends only on the size of the node level dynamics. A randomly generated academic example with 12 nodes is considered to demonstrate the efficacy of the proposed methodology.
Keywords: Static output feedback; Complex network; Decentralised control; L2 optimal

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier,
LMI approach to linear positive system analysis and synthesis,
Systems & Control Letters,
Volume 63,
2014,
Pages 50-56,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.001.
(http://www.sciencedirect.com/science/article/pii/S0167691113002156)
Abstract: This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H∞ performance of continuous-time positive systems. In addition, we further derive a new LMI for the H∞ performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H∞ performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H∞ controller synthesis for discrete-time positive systems affected by parametric uncertainties.
Keywords: Positive system; Diagonal Lyapunov matrix; LMI; Duality

Lijun Zhu, Zhiyong Chen,
Robust homogenization and consensus of nonlinear multi-agent systems,
Systems & Control Letters,
Volume 65,
2014,
Pages 50-55,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.007.
(http://www.sciencedirect.com/science/article/pii/S0167691113002594)
Abstract: In this paper, we consider consensus of a group of heterogeneous agents with nonlinear dynamics in the presence of system uncertainties. It requires that all agent states reach an agreement which is governed by specified reference dynamics. However, the reference dynamics do not generate a specific reference trajectory for feedback regulation for any agent. For this purpose, the proposed controller integrates two fundamental actions, homogenization and consensus, concurrently. On one hand, it asymptotically regulates each individual (heterogeneous, nonlinear, and uncertain) agent dynamics to the common reference dynamics using a robust homogenization technique; on the other hand, it aligns agent trajectories, asymptotically governed by the common reference dynamics, to consensus through network cooperation. The effectiveness of the controller is verified in the rigorous proof and numerical simulation.
Keywords: Multi-agent systems; Cooperative control; Heterogeneous systems; Nonlinear systems; Robust control

Jing Zhang, Jinfeng Liu,
Two triggered information transmission algorithms for distributed moving horizon state estimation,
Systems & Control Letters,
Volume 65,
2014,
Pages 1-12,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.003.
(http://www.sciencedirect.com/science/article/pii/S0167691113002557)
Abstract: In this work, we consider the reduction of information transmission frequency of distributed moving horizon estimation (DMHE) for a class of nonlinear systems in which interacting subsystems exchange information with each other through a shared communication network. Specifically, algorithms based on two event-triggered methods are proposed to reduce the number of information transmissions between the subsystems in a DMHE scheme. In the first algorithm, a subsystem sends out its current information when a triggering condition based on the difference between the current state estimate and a previously transmitted one is satisfied; in the second algorithm, the transmission of information from a subsystem to other subsystems is triggered by the difference between the current measurement of the output and its derivatives and a previously transmitted measurement. In order to ensure the convergence and ultimate boundedness of the estimation error, we also propose to redesign the local moving horizon estimator of a subsystem to account for the possible lack of state updates from other subsystems explicitly. A chemical process is utilized to demonstrate the applicability and performance of the proposed approaches.
Keywords: Nonlinear systems; Distributed state estimation; Moving horizon estimation; Information update algorithms; Chemical processes

A.Yu. Aleksandrov, Oliver Mason,
Diagonal Lyapunov–Krasovskii functionals for discrete-time positive systems with delay,
Systems & Control Letters,
Volume 63,
2014,
Pages 63-67,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.012.
(http://www.sciencedirect.com/science/article/pii/S016769111300234X)
Abstract: We consider the existence of diagonal Lyapunov–Krasovskii (L–K) functionals for positive discrete-time systems subject to time-delay. In particular, we show that the existence of a diagonal functional is necessary and sufficient for delay-independent stability of a positive linear time-delay system. We extend this result and provide conditions for the existence of diagonal L–K functionals for classes of nonlinear positive time-delay systems, which are not necessarily order preserving. We also describe sufficient conditions for the existence of common diagonal L–K functionals for switched positive systems subject to time-delay.
Keywords: Positive systems; Delay; Stability; Diagonal Lyapunov–Krasovskii functional

Hugo Leiva,
Rothe’s fixed point theorem and controllability of semilinear nonautonomous systems,
Systems & Control Letters,
Volume 67,
2014,
Pages 14-18,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.008.
(http://www.sciencedirect.com/science/article/pii/S0167691114000280)
Abstract: In this paper we apply Rothe’s fixed point theorem to prove the controllability of the following semilinear system of ordinary differential equations {z′(t)=A(t)z(t)+B(t)u(t)+f(t,z(t),u(t)),t∈(0,τ],z(0)=z0, where z(t)∈Rn, u(t)∈Rm, A(t), B(t) are continuous matrices of dimensions n×n and n×m respectively, the control function u belongs to L2=L2(0,τ;Rm) and the nonlinear function f:[0,τ]×Rn×Rm→Rn is continuous and there are a,b,c∈R and 12≤β<1 such that ‖f(t,z,u)‖Rn≤a‖z‖Rn+b‖u‖Rmβ+c,u∈Rm,z∈Rn. Under this condition we prove the following statement: if the linear ź(t)=A(t)z(t)+B(t)u(t) is controllable, then the semilinear system is also controllable on [0,τ]. Moreover, we could exhibit a control steering the nonlinear system from an initial state z0 to a final state z1 at time τ>0.
Keywords: Controllability; Nonlinear nonautonomous systems; Rothe’s fixed point theorem

Fajin Wei, Andrea Lecchini-Visintini,
On the stability of receding horizon control for continuous-time stochastic systems,
Systems & Control Letters,
Volume 63,
2014,
Pages 43-49,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.004.
(http://www.sciencedirect.com/science/article/pii/S0167691113002314)
Abstract: We study the stability of receding horizon control for continuous-time non-linear stochastic differential equations. We illustrate the results with a simulation example in which we employ receding horizon control to design an investment strategy to repay a debt.
Keywords: Receding horizon control; Stochastic differential equations; Stochastic optimal control; Hamilton–Jacobi–Bellman equations; Lyapunov functions; Itô’s formula; Optimal investment

Zhenhua Wang, Juanjuan Xu, Huanshui Zhang,
Consensusability of multi-agent systems with time-varying communication delay,
Systems & Control Letters,
Volume 65,
2014,
Pages 37-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.011.
(http://www.sciencedirect.com/science/article/pii/S0167691113002636)
Abstract: This paper studies the consensusability problem of continuous-time multi-agent systems with time-varying communication delay in undirected network. We design a consensus protocol based on the low gain solution of a parametric algebraic Riccati equation (ARE) and not use the precise information of the amount of time-varying delay. By studying the joint effect of agent dynamic and network topology, sufficient conditions are given for consensus when all poles of the system matrix are on the closed left-half plane. In case of non-zero poles on the imaginary axis, maximal admissible upper bound of the time-varying delay is given in terms of both the agent dynamic and network topology; otherwise, consensus can be achieved for the time-varying delay with arbitrarily large upper bound. Finally, simulation results are presented to demonstrate the effectiveness of the theoretical results.
Keywords: Consensusability; Consensus protocol; Undirected network; Communication delay; Parametric algebraic Riccati equation

Shiyu Zhao, Feng Lin, Kemao Peng, Ben M. Chen, Tong H. Lee,
Distributed control of angle-constrained cyclic formations using bearing-only measurements,
Systems & Control Letters,
Volume 63,
2014,
Pages 12-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.003.
(http://www.sciencedirect.com/science/article/pii/S0167691113002119)
Abstract: This paper studies distributed control of multi-vehicle formations with angle constraints using bearing-only measurements. It is assumed that each vehicle can only measure the local bearings of their neighbors and there are no wireless communications among the vehicles. The desired formation is a cyclic one, whose underlying information flow is described by an undirected cycle graph. We propose a distributed bearing-only formation control law that ensures local exponential or finite-time stability. Collision avoidance between any vehicles can be locally guaranteed in the absence of inter-vehicle distance measurements.
Keywords: Bearing-only measurement; Formation control; Cyclic formation; Finite-time stability; Lyapunov approach

M. Corless, S. Sajja, R. Shorten,
Preservation of quadratic stability under various common approximate discretization methods,
Systems & Control Letters,
Volume 63,
2014,
Pages 68-72,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.09.003.
(http://www.sciencedirect.com/science/article/pii/S0167691113001904)
Abstract: In this paper we prove the following result. If A is a Hurwitz matrix and f is a rational function that maps the open left half of the complex plane into the open unit disc, then any Hermitian matrix P>0 which is a Lyapunov matrix for A (that is, PA+A∗P<0) is also a Stein matrix for f(A) (that is, f(A)∗Pf(A)−P<0). We use this result to prove that all A-stable approximations for the matrix exponential preserve quadratic Lyapunov functions for any stable linear system. The importance of this result is that it implies that common quadratic Lyapunov functions for switched linear systems are preserved for all step sizes when discretising quadratically stable switched systems using A-stable approximations. Examples are given to illustrate our results.
Keywords: Discretization; Lyapunov matrix; Stein matrix; Quadratic stability; A-stability

David Angeli, Germán A. Enciso, Eduardo D. Sontag,
A small-gain result for orthant-monotone systems under mixed feedback,
Systems & Control Letters,
Volume 68,
2014,
Pages 9-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.002.
(http://www.sciencedirect.com/science/article/pii/S0167691114000589)
Abstract: This paper introduces a small-gain result for interconnected orthant-monotone systems for which no matching condition is required between the partial orders in input and output spaces. Previous results assumed that the partial orders adopted would be induced by positivity cones in input and output spaces and that such positivity cones should fulfill a compatibility rule: namely either be coincident or be opposite. Those two configurations correspond to positive feedback or negative feedback cases. We relax those results by allowing arbitrary orthant orders. A linear example is provided showing that the small-gain iteration used for the negative feedback case is not sufficient for global attractivity under mixed feedback. An algebraic characterization is given of the new small-gain condition, generalizing a result known in the negative feedback case. An application is given to nonlinear protein networks with one positive and one negative feedback loop.
Keywords: Systems biology; Monotone systems; Mixed feedback; Global asymptotic stability

Abdul Qayyum Khan, Muhammad Abid, Steven X. Ding,
Fault detection filter design for discrete-time nonlinear systems— A mixed ℋ−/ℋ∞ optimization,
Systems & Control Letters,
Volume 67,
2014,
Pages 46-54,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114000425)
Abstract: This work investigates the problem of designing a fault detection filter for discrete-time nonlinear systems using ℋ−/ℋ∞-optimization that simultaneously improves robustness against disturbances and enhances sensitivity to faults. Sufficient conditions for the solvability of this problem are provided in the form of a pair of coupled Hamilton–Jacobi inequalities. Both the finite-horizon and the infinite-horizon problems are addressed. The proposed methodology is elaborated through a couple of examples.
Keywords: ℋ−-index; ℋ∞-norm; Robustness; Sensitivity; Fault detection filter; Discrete-time nonlinear systems; Affine inputs

Jung Hoon Kim, Tomomichi Hagiwara,
Computing the L∞[0,h)-induced norm of a compression operator via fast-lifting,
Systems & Control Letters,
Volume 67,
2014,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114000309)
Abstract: This paper studies computing the induced norm of a compression operator defined on the Banach space L∞[0,h), which is a difficult problem since it is an infinite-rank operator. Two methods are provided for this problem, each of which can compute an upper bound and a lower bound of the induced norm by using an idea of staircase or piecewise linear approximation. Staircase approximation and piecewise linear approximation are applied through fast-lifting, by which the interval [0,h) is divided into M subintervals with equal width, and the approximation errors in these methods are ensured to be reciprocally proportional to M or M2. The effectiveness of the proposed methods is demonstrated through numerical examples.
Keywords: Compression operator; Sampled-data systems; Time-delay systems; Fast-lifting; Staircase approximation; Piecewise linear approximation

Alain Y. Kibangou,
Step-size sequence design for finite-time average consensus in secure wireless sensor networks,
Systems & Control Letters,
Volume 67,
2014,
Pages 19-23,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.010.
(http://www.sciencedirect.com/science/article/pii/S0167691114000395)
Abstract: This paper concerns the study of average consensus in wireless sensor networks with aim of providing a way to reach consensus in a finite number of steps. In particular, we investigate the design of consensus protocols when, for security reasons for instance, the underlying graph is constrained to be strongly regular or distance regular. The proposed design method is based on parameters of the intersection array characterizing the underlying graph. With this protocol, at execution time, average consensus is achieved in a number of steps equal to the diameter of the graph, i.e. the smallest possible number of steps to achieve consensus.
Keywords: Distributed algorithms; Secure wireless sensor networks; Finite-time average consensus; Distance-regular graphs

Joaquin Carrasco, William P. Heath, Alexander Lanzon,
On multipliers for bounded and monotone nonlinearities,
Systems & Control Letters,
Volume 66,
2014,
Pages 65-71,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114000231)
Abstract: Recent results in equivalence between classes of multipliers for slope-restricted nonlinearities are extended to multipliers for bounded and monotone nonlinearities. This extension requires a slightly modified version of the Zames–Falb theorem and a more general definition of phase-substitution. The results in this paper resolve apparent contradictions in the literature on classes of multipliers for bounded and monotone nonlinearities.
Keywords: Bounded and monotone nonlinearities; Zames–Falb multipliers; Absolute stability

Alexander Scheinker, Miroslav Krstić,
Extremum seeking with bounded update rates,
Systems & Control Letters,
Volume 63,
2014,
Pages 25-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.004.
(http://www.sciencedirect.com/science/article/pii/S0167691113002120)
Abstract: In this work, we present a form of extremum seeking (ES) in which the unknown function being minimized enters the system’s dynamics as the argument of a cosine or sine term, thereby guaranteeing known bounds on update rates and control efforts. We present general n-dimensional optimization and stabilization results as well as 2D vehicle control, with bounded velocity and control efforts. For application to autonomous vehicles, tracking a source in a GPS denied environment with unknown orientation, this ES approach allows for smooth heading angle actuation, with constant velocity, and in application to a unicycle-type vehicle results in control ability as if the vehicle is fully actuated. Our stability analysis is made possible by the classic results of Kurzweil, Jarnik, Sussmann, and Liu, regarding systems with highly oscillatory terms. In our stability analysis, we combine the averaging results with a semiglobal practical stability result under small parametric perturbations developed by Moreau and Aeyels.
Keywords: Adaptive control; Extremum seeking; Autonomous agents; Distributed optimization

Ettore Fornasini, Maria Elena Valcher,
Stability properties of a class of positive switched systems with rank one difference,
Systems & Control Letters,
Volume 64,
2014,
Pages 12-19,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.008.
(http://www.sciencedirect.com/science/article/pii/S0167691113002284)
Abstract: Given a single-input continuous-time positive system, described by a pair (A,b), with A a diagonal matrix, we investigate under what conditions there exists a state-feedback law u(t)=c⊤x(t) that makes the resulting controlled system positive and asymptotically stable, by this meaning that A+bc⊤ is Metzler and Hurwitz. In the second part of this note we assume that the state-space model switches among different state-feedback laws (ci⊤,i=1,2,…,p) each of them ensuring the positivity, and show that the asymptotic stability of this type of switched system is equivalent to the asymptotic stability of all its subsystems, while its stabilizability is equivalent to the existence of an asymptotically stable subsystem.
Keywords: Positive switched systems; Asymptotic stability; Stabilizability; Metzler Hurwitz matrices

Rafal Goebel,
Robustness of stability through necessary and sufficient Lyapunov-like conditions for systems with a continuum of equilibria,
Systems & Control Letters,
Volume 65,
2014,
Pages 81-88,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.014.
(http://www.sciencedirect.com/science/article/pii/S0167691114000036)
Abstract: The equivalence between robustness to perturbations and the existence of a continuous Lyapunov-like mapping is established in a setting of multivalued discrete-time dynamics for a property sometimes called semistability. This property involves a set consisting of Lyapunov stable equilibria and surrounded by points from which every solution converges to one of these equilibria. As a consequence of the main results, this property turns out to always be robust for continuous nonlinear dynamics and a compact set of equilibria. Preliminary results on reachable sets, limits of solutions, and set-valued Lyapunov mappings are included.
Keywords: Semistability; Difference inclusion; Robustness of stability; Set-valued Lyapunov function

Martin Gugat,
Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term,
Systems & Control Letters,
Volume 66,
2014,
Pages 72-84,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114000279)
Abstract: We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.
Keywords: Boundary feedback; Hyperbolic partial differential equation; Exponential stability; Decay rate; Telegraph equation; Nonlinear wave equation; Damping; Anti-damping; Semilinear wave equation

Błażej Cichy, Krzysztof Gałkowski, Eric Rogers,
2D systems based robust iterative learning control using noncausal finite-time interval data,
Systems & Control Letters,
Volume 64,
2014,
Pages 36-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.002.
(http://www.sciencedirect.com/science/article/pii/S0167691113002168)
Abstract: This paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.
Keywords: Iterative learning control; Robust control; 2D systems; Noncausal data


Editorial Board,
Systems & Control Letters,
Volume 63,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(13)00244-2.
(http://www.sciencedirect.com/science/article/pii/S0167691113002442)

Kun Liu, Emilia Fridman,
Delay-dependent methods and the first delay interval,
Systems & Control Letters,
Volume 64,
2014,
Pages 57-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.005.
(http://www.sciencedirect.com/science/article/pii/S0167691113002363)
Abstract: This paper deals with the solution bounds for time-delay systems via delay-dependent Lyapunov–Krasovskii methods. Solution bounds are widely used for systems with input saturation caused by actuator saturation or by the quantizers with saturation. We show that an additional bound for solutions is needed for the first time-interval, where t<τ(t), both in the continuous and in the discrete time. This first time-interval does not influence on the stability and the exponential decay rate analysis. The analysis of the first time-interval is important for nonlinear systems, e.g., for finding the domain of attraction. Regional stabilization of a linear (probably, uncertain) system with unknown and bounded input delay under actuator saturation is revisited, where the saturation avoidance approach is used.
Keywords: Time-varying delay; Lyapunov–Krasovskii method; First delay interval; Input saturation

Bao-Zhu Guo, Liang Zhang,
Local null controllability for a chemotaxis system of parabolic–elliptic type,
Systems & Control Letters,
Volume 65,
2014,
Pages 106-111,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.010.
(http://www.sciencedirect.com/science/article/pii/S0167691113002326)
Abstract: We consider the controllability of a chemotaxis system of parabolic–elliptic type. By linearizing the nonlinear system into two separate linear equations, we can bypass the obstacle caused by the nonlinear drift term and establish local null controllability of the original nonlinear system. This approach is different from the usual method for dealing with coupled parabolic systems.
Keywords: Local null controllability; Chemotaxis system; Parabolic–elliptic type; Kakutani’s fixed-point theorem

Liu Liu, Yufeng Lu,
Stabilizability, representations and factorizations for time-varying linear systems,
Systems & Control Letters,
Volume 66,
2014,
Pages 58-64,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.008.
(http://www.sciencedirect.com/science/article/pii/S0167691113002600)
Abstract: We study the system representations, factorizations and stabilizability of a discrete-time time-varying linear system in the framework of nest algebra. We shown that every time-varying linear system admits a normalized left factorization, while it may possibly not have a right factorization. The relationship between the system representation and factorization is studied, and some new stabilizability criteria are established.
Keywords: Normalized factorization; Representation; Stabilizability; Time-varying system; Nest algebra

Matthew Ellis, Jing Zhang, Jinfeng Liu, Panagiotis D. Christofides,
Robust moving horizon estimation based output feedback economic model predictive control,
Systems & Control Letters,
Volume 68,
2014,
Pages 101-109,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114000590)
Abstract: In this work, we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise. In order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise, a deterministic (high-gain) observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value; after this initial small time period, a robust moving horizon estimation scheme is used on-line to provide more accurate and smoother state estimates. In the design of the robust moving horizon estimation scheme, the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state. Within the confidence regions, the moving horizon estimation scheme is allowed to optimize its estimates. The output feedback economic model predictive controller is designed via Lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme. The stability of the closed-loop system is analyzed rigorously and conditions that ensure the closed-loop stability are derived. Extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach.
Keywords: Model predictive control; Economic optimization; State estimation; Nonlinear systems; Process control; Process economics

Srinivasan Krishnaswamy, Harish K. Pillai,
On the number of special feedback configurations in linear modular systems,
Systems & Control Letters,
Volume 66,
2014,
Pages 28-34,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.018.
(http://www.sciencedirect.com/science/article/pii/S0167691114000073)
Abstract: This paper deals with a state feedback in linear modular systems (LMSs) defined over a finite field Fq. By means of a state feedback, any controllable LMS S can be converted to a closed loop system having a desired characteristic polynomial p(s). Given a polynomial p(s), we calculate the number of state feedback matrices which result in single input controllable closed loop systems having a characteristic polynomial p(s).
Keywords: Linear modular systems; Pole placement; State feedback

Dequan Li, Qiupeng Liu, Xiaofan Wang, Zhixiang Yin,
Quantized consensus over directed networks with switching topologies,
Systems & Control Letters,
Volume 65,
2014,
Pages 13-22,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.013.
(http://www.sciencedirect.com/science/article/pii/S0167691113002521)
Abstract: This paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies. We propose an effective distributed protocol with an adaptive finite-level uniform quantized strategy, under which consensus among agents is guaranteed with weaker communication conditions. In particular, we analytically prove that each agent sending 5-level quantized information to each of its neighbors, together with 3-level quantized information to itself at each time step, which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded. By dropping the typical common left eigenvector requirement for the existence of common quadratic Lyapunov function, we conduct the convergence analysis based on the notion of input-to-output stability. The proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability, and it fits well into the digital network framework.
Keywords: Consensus; Multi-agent systems; Uniform quantization; Digraph; Switching networks

Yujuan Han, Wenlian Lu, Zhe Li, Tianping Chen,
Pinning dynamic systems of networks with Markovian switching couplings and controller–node set,
Systems & Control Letters,
Volume 65,
2014,
Pages 56-63,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.012.
(http://www.sciencedirect.com/science/article/pii/S0167691113002648)
Abstract: In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller–node set. Here, the coupling matrices and the controller–node sets change with time, induced by a continuous-time Markov chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponential stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller–node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable subsystems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.
Keywords: Pinning control; Coupled dynamical system; Markovian switching; Spatial pinning control

Aolo Bashar Abusaksaka, Jonathan R. Partington,
BIBO stability of some classes of delay systems and fractional systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 43-46,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.009.
(http://www.sciencedirect.com/science/article/pii/S0167691113002405)
Abstract: A new test is presented for the BIBO stability of delay systems of neutral type with a single delay, specified in terms of their transfer functions, enabling us to decide on some cases that were previously open. Next, a class of fractional systems is considered, and a method is given for determining the stability intervals for such systems.
Keywords: Delay system; Fractional system; BIBO stability; H∞ stability; Asymptotic stability

Mazen Farhood, Carolyn L. Beck,
On the balanced truncation and coprime factors reduction of Markovian jump linear systems,
Systems & Control Letters,
Volume 64,
2014,
Pages 96-106,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.004.
(http://www.sciencedirect.com/science/article/pii/S0167691113002569)
Abstract: The paper deals with the balanced truncation and coprime factors reduction of Markovian jump linear (MJL) systems, which can have mode-varying state, input, and output dimensions. We develop machinery for balancing mean square stable MJL system realizations using generalized Gramians and strict Lyapunov inequalities, and provide an improved a priori upper bound on the error induced in the balanced truncation process. We also generalize the coprime factors reduction method and, in doing so, extend the applicability of the balanced truncation technique to the class of mean square stabilizable and detectable MJL systems. We provide tools to establish mean square stabilizability and detectability of the considered MJL systems. In addition, a notion of right-coprime factorization of MJL systems and methods to construct such factorizations are given. The error measure in the coprime factors reduction approach, while still norm-based, does not directly capture the mismatch between the nominal system and the reduced-order model, as is the case in the balanced truncation approach where mean square stable models are considered. Instead, the error measure is given in terms of the distance between the coprime factors realizations, and thus has an interpretation in terms of robust feedback stability. The paper concludes with an illustrative example which demonstrates how to apply the coprime factors model reduction approach.
Keywords: Markovian jump linear systems; Balanced truncation; Coprime factors reduction; Model reduction

Daniel Franco, Hartmut Logemann, Juan Perán,
Global stability of an age-structured population model,
Systems & Control Letters,
Volume 65,
2014,
Pages 30-36,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.012.
(http://www.sciencedirect.com/science/article/pii/S016769111300251X)
Abstract: We consider a nonlinear discrete-time population model for the dynamics of an age-structured species. This model has the form of a Lure feedback system (well-known in control theory) and is a particular case of the system studied by Townley et al. in Townley et al. (2012). The main objective is to show that, in this case, the range of nonlinearities for which the existence of globally asymptotically stable non-zero equilibrium can be guaranteed is considerably larger than that in the main result in Townley et al. (2012). We illustrate our results with several biologically meaningful examples.
Keywords: Age-structured species; Feedback systems; Global stability; Lure systems; Population dynamics

Lijian Xu, Le Yi Wang, George Yin, Wei Xing Zheng,
Enhanced feedback robustness against communication channel multiplicative uncertainties via scaled dithers,
Systems & Control Letters,
Volume 68,
2014,
Pages 25-32,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.03.001.
(http://www.sciencedirect.com/science/article/pii/S0167691114000577)
Abstract: In this paper, a new method is introduced to enhance feedback robustness against communication gain uncertainties. The method employs a fundamental property in stochastic differential equations to add a scaled stochastic dither under which tolerable gain uncertainties can be much enlarged, beyond the traditional deterministic optimal gain margin. Algorithms, stability, convergence, and robustness are presented for first-order systems. Extension to higher-dimensional systems is further discussed. Simulation results are used to illustrate the merits of this methodology.
Keywords: Feedback robustness; Communication channels; Gain uncertainty; Dithers; Itô’s formula; Stochastic differential equations

D. Sui, T.A. Johansen,
Linear constrained moving horizon estimator with pre-estimating observer,
Systems & Control Letters,
Volume 67,
2014,
Pages 40-45,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.003.
(http://www.sciencedirect.com/science/article/pii/S0167691114000413)
Abstract: In this paper, a constrained moving horizon estimation (MHE) strategy for linear systems is proposed. Recently, the use of a pre-estimating linear observer in the forward prediction equations in the MHE cost function has been proposed in order to reduce the effects of uncertainty. Here we introduce state constraints within this formulation and investigate stability properties in the presence of bounded disturbances and noise. The robustness and performance of the proposed observer is demonstrated with a simulation example.
Keywords: Moving horizon estimation; State constraints; Input-to-state stability

Vakhtang Lomadze,
Characterization of linear differential systems (in several variables),
Systems & Control Letters,
Volume 68,
2014,
Pages 20-24,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.011.
(http://www.sciencedirect.com/science/article/pii/S0167691114000656)
Abstract: We show that a set of smooth trajectories is the solution set of a linear constant coefficient partial differential equation if and only if it is linear, shift-invariant and complete. (By completeness, we mean exactly what Willems called jet-completeness in his Automatica paper in 1986.)
Keywords: LTID system; Jet; Complete


Editorial Board,
Systems & Control Letters,
Volume 64,
2014,
Page IFC,
ISSN 0167-6911,
https://doi.org/10.1016/S0167-6911(14)00014-0.
(http://www.sciencedirect.com/science/article/pii/S0167691114000140)

César C. Scharlau, Mauricio C. de Oliveira, Alexandre Trofino, Tiago J.M. Dezuo,
Switching rule design for affine switched systems using a max-type composition rule,
Systems & Control Letters,
Volume 68,
2014,
Pages 1-8,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.007.
(http://www.sciencedirect.com/science/article/pii/S0167691114000462)
Abstract: This paper presents conditions for designing a switching rule that drives the state of the switched dynamic system to a desired equilibrium point. The proposed method deals with the class of switched systems where each subsystem has an affine vector field and considers a switching rule using ‘max’ composition. The results guarantee global asymptotic stability of the tracking error dynamics even if sliding mode occurs at any switching surface of the system. In addition, the method does not require a Hurwitz convex combination of the dynamic matrices of the subsystems. Two numerical examples are used to illustrate the results.
Keywords: Affine switched systems; Switching rule design; Sliding mode; Lyapunov function

Juri Belikov, Ülle Kotta, Maris Tõnso,
Comparison of LPV and nonlinear system theory: A realization problem,
Systems & Control Letters,
Volume 64,
2014,
Pages 72-78,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.009.
(http://www.sciencedirect.com/science/article/pii/S0167691113002296)
Abstract: The paper explores the utilization of the nonlinear realization theory to address the problem of transforming linear parameter-varying input–output (LPV-IO) equations into a state-space form with static dependence on the so-called scheduling parameter. The necessary and sufficient solvability conditions are given, and three additional subclasses of LPV-IO equations are suggested that are guaranteed to have a realization of the considered type.
Keywords: Nonlinear systems; Linear parameter-varying systems; State-space realization; Polynomial methods

Kaien Liu, Guangming Xie, Long Wang,
Containment control for second-order multi-agent systems with time-varying delays,
Systems & Control Letters,
Volume 67,
2014,
Pages 24-31,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.013.
(http://www.sciencedirect.com/science/article/pii/S0167691114000024)
Abstract: This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.
Keywords: Containment control problem; Multi-agent systems; Time-varying delays; Digraph

Bin Liu, Chunxia Dou, David J. Hill,
Robust exponential input-to-state stability of impulsive systems with an application in micro-grids,
Systems & Control Letters,
Volume 65,
2014,
Pages 64-73,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.005.
(http://www.sciencedirect.com/science/article/pii/S0167691113002570)
Abstract: This paper studies the robust exponential input-to-state stability (robust e-ISS) for impulsive systems. New notions of input-to-state exponent (IS-e) and e-property are proposed. Based on the established relation between IS-e and e-property, and the method of variation of constants formula, the equivalent conditions for robust e-ISS have been derived. Then the notion of robust event-e-ISS is defined. The sufficient conditions and the robust regions for robust e-ISS and robust event-e-ISS are also derived by using the IS-e of every subsystem. It shows the whole system may have robust event-e-ISS while every subsystem may have no ISS. It also shows the external disturbances may lead to relatively small robust regions. The results are then specialized to derive the equivalent conditions of interval e-ISS for interval impulsive systems. As an application, the result is used to test the ISS for a controlled micro-grid.
Keywords: Robust exponential ISS (robust e-ISS); Input-to-state exponent (IS-e); Impulsive system; Uncertainty; Micro-grid

Maria Elena Valcher, Pradeep Misra,
On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions,
Systems & Control Letters,
Volume 66,
2014,
Pages 94-103,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.01.006.
(http://www.sciencedirect.com/science/article/pii/S0167691114000267)
Abstract: The aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents, under the assumption that their mutual interactions can be described by a weighted, signed, connected and structurally balanced communication graph. This amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative, and hence represented by nonnegative weights, while interactions between agents belonging to opposite groups are antagonistic, and hence represented by nonpositive weights. In this framework, bipartite consensus can always be reached under the stabilizability assumption on the state-space model describing the dynamics of each agent. On the other hand, (nontrivial) standard consensus may be achieved only under very demanding requirements, both on the Laplacian associated with the communication graph and on the agents’ description. In particular, consensus may be achieved only if there is a sort of “equilibrium” between the two groups, both in terms of cardinality and in terms of the weights of the “conflicting interactions” amongst agents.
Keywords: Consensus; Bipartite consensus; Multi-agents; Antagonistic interactions; Communication graph

John W. Simpson-Porco, Francesco Bullo,
Contraction theory on Riemannian manifolds,
Systems & Control Letters,
Volume 65,
2014,
Pages 74-80,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.016.
(http://www.sciencedirect.com/science/article/pii/S016769111400005X)
Abstract: Contraction theory is a methodology for assessing the stability of trajectories of a dynamical system with respect to one another. In this work, we present the fundamental results of contraction theory in an intrinsic, coordinate-free setting, with the presentation highlighting the underlying geometric foundation of contraction theory and the resulting stability properties. We provide coordinate-free proofs of the main results for autonomous vector fields, and clarify the assumptions under which the results hold. We state and prove several interesting corollaries to the main result, study cascade and feedback interconnections of contracting systems, study some simple examples, and highlight how contraction theory has arisen independently in other scientific disciplines. We conclude by illustrating the developed theory for the case of gradient dynamics.
Keywords: Contraction theory; Incremental stability; Differential geometric methods; Nonlinear control

L.Q. Thuan, M.K. Camlibel,
On the existence, uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems,
Systems & Control Letters,
Volume 68,
2014,
Pages 76-85,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2014.02.009.
(http://www.sciencedirect.com/science/article/pii/S0167691114000620)
Abstract: In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions.
Keywords: Piecewise affine systems; Well-posedness; Existence and uniqueness of solutions; Carathéodory solutions; Filippov solutions; One-sided Lipschitz condition

Vasile Dragan, Samir Aberkane,
H2 optimal filtering for continuous-time periodic linear stochastic systems with state-dependent noise,
Systems & Control Letters,
Volume 66,
2014,
Pages 35-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.020.
(http://www.sciencedirect.com/science/article/pii/S0167691114000103)
Abstract: This note addresses the problem of optimal H2 filtering for a class of continuous-time time-varying stochastic systems. The time-variation character is considered to be periodic. The state space representation of the optimal filter is designed based on the unique periodic solution of a suitable Lyapunov differential equation and the periodic and stabilizing solution of a suitable generalized periodic Riccati differential equation. Some numerical experiments are also added to show the effectiveness of the proposed method.
Keywords: H2 norm; Periodic stochastic systems; Filtering; Lyapunov differential equations; Riccati differential equations

Ti-Jun Xiao, Yuming Zhang,
Lack of exponential decay in viscoelastic materials with voids,
Systems & Control Letters,
Volume 63,
2014,
Pages 39-42,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.11.006.
(http://www.sciencedirect.com/science/article/pii/S0167691113002375)
Abstract: We study the stability of solutions to a coupled evolution system associated with an isotropic porous and centrosymmetric viscoelastic solid with porous dissipation (a porous elastic system with history). With the help of the method of the semigroup theory and some novel observations, we prove successfully that the condition of equal wave-speed propagation is still necessary for exponential stability of the system in the case of Dirichlet–Dirichlet boundary conditions.
Keywords: Porous elastic systems with history; Semigroup method; Exponential stability

Ian R. Manchester, Jean-Jacques E. Slotine,
Transverse contraction criteria for existence, stability, and robustness of a limit cycle,
Systems & Control Letters,
Volume 63,
2014,
Pages 32-38,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.10.005.
(http://www.sciencedirect.com/science/article/pii/S0167691113002132)
Abstract: This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimisation tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including the preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for interconnected systems via LMI conditions on component subsystems.
Keywords: Nonlinear systems; Stability; Contraction; Limit cycles; Sum-of-squares; Convex optimisation

Weiyin Fei, Hongjian Liu, Wei Zhang,
On solutions to fuzzy stochastic differential equations with local martingales,
Systems & Control Letters,
Volume 65,
2014,
Pages 96-105,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.009.
(http://www.sciencedirect.com/science/article/pii/S0167691113002612)
Abstract: This paper deals with a class of fuzzy stochastic differential equations (FSDEs) driven by a continuous local martingale under the Lipschitzian condition. Such equations can be useful in modeling hybrid systems, where the phenomena are simultaneously subjected to two kinds of uncertainties: randomness and fuzziness. The solutions of the FSDEs are the fuzzy stochastic processes, and their uniqueness is considered to be in a strong sense. Thus, the existence and uniqueness of solutions to the FSDEs under the Lipschitzian condition is first proven. Moreover, some asymptotic properties of the solutions to the FSDEs are investigated. Finally, an illustrating example on the interest term model is provided.
Keywords: Fuzzy stochastic differential equation (FSDE); Fuzzy stochastic Itô integral; Local martingales; Fuzzy random variables; Lipschitzian condition; Interest term model

R.V. Adams,
Infinitesimal perturbation analysis of a multi-stage tandem of fluid queue with additive loss feedback,
Systems & Control Letters,
Volume 66,
2014,
Pages 22-27,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.017.
(http://www.sciencedirect.com/science/article/pii/S0167691114000061)
Abstract: In this paper Infinitesimal Perturbation Analysis (IPA) is used to derive the gradient estimators for loss volume and queue workload in a multi-stage tandem of stochastic fluid queues with instantaneous additive loss-feedback for overall congestion control. These gradient estimators are then used to drive a standard stochastic approximation algorithm to optimize, with respect to the buffer limits of the individual queues, an objective function which is the weighted sum of loss volume and queue workload of the queues that make up the tandem.
Keywords: Infinitesimal perturbation analysis; IPA; Stochastic fluid models; Stochastic optimization; Queueing networks; Congestion control

Yuhong Xu,
Stochastic maximum principle for optimal control with multiple priors,
Systems & Control Letters,
Volume 64,
2014,
Pages 114-118,
ISSN 0167-6911,
https://doi.org/10.1016/j.sysconle.2013.12.001.
(http://www.sciencedirect.com/science/article/pii/S0167691113002533)
Abstract: The necessary condition is derived for optimal control with multiple priors which are mutually singular. The tool we use is the theory of G-expectation.
Keywords: Stochastic maximum principle; Multiple priors; G-expectation; G-Brownian motion