Adaptive Control of Parabolic PDEs

Andrey Smyshlyaev and Miroslav Krstic


Princeton University Press, 2010      

344 pages, hardcover

ISBN-13: 978-0691142869


Preface and Contents




1. Introduction


Part I. Non-Adaptive Controllers

2. State Feedback

3. Closed-Form Controllers

4. Observers

5. Output Feedback

6. Control of Complex-Valued PDEs


Part II. Adaptive Schemes

7. Systematization of Approaches to Adaptive Boundary Stabilization of PDEs

8. Lyapunov-Based Designs

9. Certainty Equivalence Design with Passive Identifiers

10. Certainty Equivalence Design with Swapping Identifiers

11. State Feedback for PDEs with Spatially Varying Coefficients

12. Closed-Form Adaptive Output-Feedback Controllers

13. Output Feedback for PDEs with Spatially Varying Coefficients

14. Inverse Optimal Control






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Publisher's description:


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.


"Unique and excellent, this book systematically and rigorously develops design and analysis tools and clearly explains technical concepts. As the first book to cover its topics, it significantly expands the scope of adaptive control knowledge. I strongly recommend this book as either a reference or an advanced textbook for researchers and graduate students who study and work in engineering and applied sciences." – Gang Tao, University of Virginia