Adaptive Backstepping Control of Uncertain Systems Nonsmooth Nonline

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Jing Zhou, Changyun Wen

Adaptive Backstepping Control of Uncertain Systems Nonsmooth Nonlinearities, Interactions or Time-Variations

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Series Advisory Board F. Allgöwer, P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis

Authors Jing Zhou Department of Engineering Cybernetics Faculty of Information Technology, Mathematics and Electrical Engineering Norwegian University of Science and Technology O.S. Bragstads plass 2d 7491 Trondheim, Norway Email: [email protected]

Changyun Wen School of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue 639798 Singapore Email: [email protected]

ISBN 978-3-540-77806-6

e-ISBN 978-3-540-77807-3

DOI 10.1007/978-3-540-77807-3 Lecture Notes in Control and Information Sciences

ISSN 0170-8643

Library of Congress Control Number: 2007943052 c 2008 

Springer-Verlag Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed in acid-free paper 543210 springer.com

To Feng Zhou, Lingfang Ma, Xiaozhong Shen and Zhile Shen J. Zhou

To Xiu Zhou, Wen, Wendy, Qingyun and Qinghao C. Wen

Preface

This book presents new methodologies for the design and analysis of adaptive control systems based on the backstepping approach. Our emphasis is on dynamic uncertain systems with nonsmooth nonlinearities, such as backlash, deadzone, hysteresis and saturation, or time-varying parameters, or interactions. The backstepping approach, a recursive Lyapunov-based scheme, was proposed in the beginning of 1990s. With this method the construction of feedback control laws and Lyapunov functions is systematic, following a step-by-step algorithm. Backstepping can be used to relax the matching condition, which blocked the traditional Lyapunov-based design. A major advantage of backstepping is that it has the flexibility to avoid cancellations of useful nonlinearities and achieve regulation and tracking properties. The technique was comprehensively addressed by Krstic, Kanellakopoulos and Kokotovic in [1]. However, there is still no monograph available to address problems such as the handling of nonsmooth nonlinearities, time varying parameter