E-Book Overview
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.
E-Book Content
Adaptive Control of Parabolic PDEs This page intentionally left blank Adaptive Control of Parabolic PDEs Andrey Smyshlyaev and Miroslav Krstic PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD c 2010 by Princeton University Press Copyright Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved Library of Congress Cataloging-in-Publication Data Smyshlyaev, Andrey. Adaptive control of parabolic PDEs / Andrey Smyshlyaev and Miroslav Krstic. p. cm. Includes bibliographical references and index. ISBN 978-0-691-14286-9 (hardcover : alk. paper) 1. Differential equations, Parabolic. 2. Distributed parameter systems. 3. Adaptive control systems. I. Krstic, Miroslav. II. Title. QA374.S59 2010 515 .3534—dc22 2009048242 British Library Cataloging-in-Publication Data is available This book has been composed in Times Printed on acid-free paper. ∞ Typeset by S R Nova Pvt Ltd, Bangalore, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Contents Preface ix Chapter 1. Introduction 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 PART I Parabolic and Hyperbolic PDE Systems The Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters Class of Parabolic PDE Systems Backstepping Explicitly Parametrized Controllers Adaptive Control Overview of the Literature on Adaptive Control for Parabolic PDEs Inverse Optimality Organization of the Book Notation NONADAPTIVE CONTROLLERS Chapter 2. State Feedback 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Problem Formulation Backstepping Transformation and PDE for Its Kernel Converting the PDE into an Integral Equation Analysis of the Integral Equation by Successive Approximation Series Stability of the Closed-Loop System Dirichlet Uncontrolled End Neumann Actuation Simulation Discussion Notes and References Chapter 3. Closed-Form Controllers 3.1 3.2 3.3 3.4 The Reaction-Diffusion Equation A Family of Plants with Spatially Varying Reactivity Solid Propellant Rocket Model Plants with Spatially Varying Diffusivity 1 2 3 4 5 5 6 7 7 9 11 13 13 14 17 19 22 24 26 27 27 33 35 35 38 40 42 vi CONTENTS 3.5 3.6 3.7 3.8 The Time-Varying Reaction Equation More Complex Systems 2D and 3D Systems Notes and References Chapter 4. Observers 4.1 4.2 4.3 4.4 Observer Design for the Ant