Delay Compensation for Nonlinear, Adaptive, and PDE Systems
Miroslav Krstic

Birkhauser, 2009        

466 pages, hardcover

ISBN-13: 978-0-8176-4698-1


Preface and Contents




1. Introduction


Part I. Linear Delay-ODE Cascades

2. Basic Predictor Feedback

3. Predictor Observers

4. Inverse Optimal Redesign

5. Robustness to Delay Mismatch

6. Time-Varying Delay


Part II. Adaptive Control

7. Delay-Adaptive Full-State Predictor Feedback

8. Delay-Adaptive Predictor with Estimation of Actuator State

9. Trajectory Tracking Under Unknown Delay and ODE Parameters


Part III. Nonlinear Systems

10. Nonlinear Predictor Feedback

11. Forward-Complete Systems

12. Strict- Feedforward Systems

13. Linearizable Strict-Feedforward Systems


Part IV. PDE-ODE Cascades

14. ODEs with General Transport-Like Actuator Dynamics

15. ODEs with Heat PDE Actuator Dynamics

16. ODEs with Wave PDE Actuator Dynamics

17. Observers for ODEs Involving PDE Sensor and Actuator Dynamics


Part V. Delay-PDE and PDE-PDE Cascades

18. Unstable Reaction-Diffusion PDE with Input Delay

19. Antistable Wave PDE with Input Delay

20. Other PDE-PDE Cascades






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Publisher's description:


Some of the most common dynamic phenomena that arise in engineering practice—actuator and sensor delays—fall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systems, the Smith predictor, has remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems.


The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.


Specific features and topics include:


·   A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback.

·   A detailed treatment of individual classes of problems—nonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delays—will help the reader master the techniques presented.

·   Numerous examples ease a student new to delay systems into the topic.

·   Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs.

·   The basics of Poincaré and Agmon inequalities, Lyapunov input-to-state stability, parameter projection for adaptive control, and Bessell functions are summarized in appendices for the reader’s convenience.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Written for: graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering