Adaptive Control of Parabolic PDEs

Princeton University Press
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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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About the author

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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Additional Information

Publisher
Princeton University Press
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Published on
Jul 1, 2010
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Pages
344
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ISBN
9781400835362
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Best For
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Language
English
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Genres
Mathematics / Applied
Mathematics / Differential Equations / General
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Content Protection
This content is DRM protected.
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Eligible for Family Library

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With Wiley’s Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including:

• Embedded & searchable equations, figures & tables
• Math XML
• Index with linked pages numbers for easy reference
• Redrawn full color figures to allow for easier identification

Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students.

The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal twoï¿1?2 or threeï¿1?2 semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
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 and input-to-state stability, parameter projection for adaptive control, and Bessel 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.

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