Stochastic Averaging and Stochastic Extremum
Seeking
Shu-Jun
Liu and Miroslav Krstic
Springer, 2012
224 pages, hardcover
ISBN 978-1-4471-4086-3
Contents:
Preface
1. Introduction
to Averaging
2. Introduction
to Extremum Seeking
3. Stochastic
Averaging for Asymptotic Stability
4. Stochastic
Averaging for Practical Stability
5. Single-parameter
Stochastic Extremum Seeking
6. Stochastic
Source Seeking for Nonholonomic Vehicles
7. Stochastic
Source Seeking with Tuning of Forward Velocity
8. Multi-parameter
Stochastic Extremum Seeking and Slope Seeking
9. Stochastic
Nash Equilibrium Seeking for Games with General Nonlinear Payoffs
10. Nash
Equilibrium Seeking for Quadratic Games and Application to Oligopoly Markets
and Vehicle Deployment
11. Newton-based
Stochastic Extremum Seeking.
Appendices
References
Index
Publisher's
description:
Stochastic
Averaging and Stochastic Extremum Seeking develops methods of mathematical
analysis inspired by the interest in reverse engineering and analysis of
bacterial convergence by chemotaxis and to apply similar stochastic
optimization techniques in other environments.
The first half of
the text presents significant advances in stochastic averaging theory,
necessitated by the fact that existing theorems are restricted to systems with
linear growth, globally exponentially stable average models, vanishing
stochastic perturbations, and prevent analysis over infinite time horizon.
The second half
of the text introduces stochastic extremum seeking algorithms for model-free
optimization of systems in real time using stochastic perturbations for
estimation of their gradients. Both gradient- and Newton-based algorithms are
presented, offering the user the choice between the simplicity of
implementation (gradient) and the ability to achieve a known, arbitrary
convergence rate (Newton).
The design of
algorithms for non-cooperative/adversarial games is described. The analysis of
their convergence to Nash equilibria is provided. The algorithms are
illustrated on models of economic competition and on problems of the deployment
of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E.
coli, is explored with the aim of identifying two simple feedback laws for
climbing nutrient gradients. Stochastic extremum seeking is shown to be a
biologically plausible interpretation for chemotaxis. For the same
chemotaxis-inspired stochastic feedback laws, the book also provides a detailed
analysis of convergence for models of nonholonomic robotic vehicles operating
in GPS-denied environments.