Advanced Topics in Nonlinear Control Systems

WORLD SCIENTIFIC SERIES ON

^Wfl fll3il:*31l3fli Series Editor: Leon 0. Chua

ADVANCED TOPICS IN NONLINEAR CONTROL SYSTEMS Editors

T. P. Leung & H. S. Qin

World Scientific

ADVANCED TOPICS IN NONLINEAR CONTROL SYSTEMS

WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE Editor: Leon O. Chua University of California, Berkeley Series A.

MONOGRAPHS AND TREATISES

Volume 23:

Nonlinear Dynamics in Particle Accelerators R. Dilao & R. Alves-Pires

Volume 24:

From Chaos to Order G. Chen & X. Dong

Volume 25:

Chaotic Dynamics in Hamiltonian Systems H. Dankowicz Visions of Nonlinear Science in the 21st Century J. L Huertas, W.-K. Chen & R. N. Madan The Thermomechanics of Nonlinear Irreversible Behaviors — An Introduction G. A. Maugin

Volume 26: Volume 27:

Volume 28:

Applied Nonlinear Dynamics & Chaos of Mechanical Systems with Discontinuities Edited by M. Wiercigroch & B. de Kraker

Volume 29:

Nonlinear & Parametric Phenomena* V. Damgov

Volume 30:

Quasi-Conservative Systems: Cycles, Resonances and Chaos A. D. Morozov

Volume 31:

CNN: A Paradigm for Complexity L. O. Chua From Order to Chaos II L P. Kadanoff Lectures in Synergetics V. I. Sugakov

Volume 32: Volume 33: Volume 34:

Introduction to Nonlinear Dynamics* L Kocarev & M. P. Kennedy

Volume 35:

Introduction to Control of Oscillations and Chaos A. L. Fradkov & A. Yu. Pogromsky

Volume 36:

Chaotic Mechanics in Systems with Impacts & Friction B. Blazejczyk-Okolewska, K. Czolczynski, T. Kapitaniak & J. Wojewoda

Volume 37:

Invariant Sets for Windows — Resonance Structures, Attractors, Fractals and Patterns A. D. Morozov, T. N. Dragunov, S. A. Boykova & O. V. Malysheva

Volume 38:

Nonlinear Noninteger Order Circuits & Systems — An Introduction P. Arena, R. Caponetto, L Fortuna & D. Porto

Volume 39:

The Chaos Avant-Garde: Memories of the Early Days of Chaos Theory Edited by Ralph Abraham & Yoshisuke Ueda

*Forthcoming

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H. S.Qin Academia Sinica, PRC

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Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ADVANCED TOPICS IN NONLINEAR CONTROL SYSTEMS Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN 981-02-4442-8

Printed in Singapore.

Preface This work results from the joint collabration of several researchers who are interested in the recent development of nonlinear control theory. For the last fifty years, a number of textbooks and monographs on nonlinear control theory and design methods have been published. For example, phase plane analysis and describing function are well known in classical control theory. In modern control there are those related with optimal control, using differential geometry and differential algebra methods, variable structure control, Hinfinity control and so on. These have been useful in promoting the advancement of automatic control science and technology. Since 1990 there have been a number of new results and contributions in the area. In view of such, the authors of this book have an aspiration to introduce these to interested readers for arousing broader attention and discussion. Since most systems are nonlinear by nature, such study would have its own significance. This book is mainly targeted at researchers and it can also be of interest to automation engineers. It would be of paramount importance that advanced control theories could eventually be adapted for real engineering applications. This book consists of six chapters. Chapter 1 is devoted to presenting the fundamental theory, the main properties and control aspects for generalized forced Hamiltonian systems. Chapter 2 presents recently developed theories of static and dynamic output feedback stabilization methodology, and design of dynamic compensator for nonlinear control systems. Chapter 3 contains new contributions of developing basic principles for the design and construction of controller for continuous finite-time control systems. In Chapter 4 there are descriptions of modelling, control and simulation of a class of hybrid systems. Chapter 5 deals with the robust and adaptive control of nonlinear systems with nonholonomic constraints, with a case study of constrained robot control. Chapter 6 is concerned with chaos control of nonlinear systems. It concludes theory and modelling of resulting chaos, controlling chaos and synchronizing chaos for nonlinear systems with two or even higher than two dimensions. It is hoped that such coverage will provide readers a rather comprehensive review of some important developments of advanced nonlinear control theory in recent years.

T.P.Leung and H.S.Qin

Contents PREFACE CHAPTER 1 GENERALIZED HAMILTONIAN SYSTEMS D. Cheng 1.1 Introduction 1.2 From Newton's second law to Hamiltonian equation 1.3 Symplectic manifold and Poisson manifold 1.4 Pseudo-Hamiltonian systems and controlled pseudo-Hamiltonian systems 1.5 Pseudo-Poisson manifold 1.6 Integrability 1.7