Adaptive Control of Parabolic PDEs

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Princeton University Press, Jul 1, 2010 - Mathematics - 344 pages
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This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others.

Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.

 

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Contents

Chapter 1 Introduction
1
NONADAPTIVE CONTROLLERS
11
ADAPTIVE SCHEMES
109
Appendix A Adaptive Backstepping for Nonlinear ODEsThe Basics
277
Appendix B Poincaré and Agmon Inequalities
305
Appendix C Bessel Functions
307
Appendix D Barbalats and Other Lemmas for Proving Adaptive Regulation
310
Appendix E Basic Parabolic PDEs and Their Exact Solutions
313
References
317
Index
327
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About the author (2010)

Andrey Smyshlyaev is assistant project scientist at the University of California, San Diego. Miroslav Krstic is the Sorenson Distinguished Professor and the founding director of the Cymer Center for Control Systems and Dynamics at the University of California, San Diego. Smyshlyaev and Krstic are the authors of "Boundary Control of PDEs".

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