Adaptive Control Systems Adaptive Control Systems GANG FENG and ROGELIO LOZANO OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Newnes An imprint ofButterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801±2041 A division ofReed Educational and Professional Publishing Ltd A member ofthe Reed Elsevier plc group First published 1999 # Reed Educational and Professional Publishing Ltd 1999 All rights reserved. No part ofthis publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission ofthe copyright holder except in accordance with the provisions ofthe Copyright, Designs and Patents Act 1988 or under the terms ofa licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Rd, London, England W1P 9HE. Applications for the copyright holder's written permission to reproduce any part ofthis publication should be addressed to the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 07506 3996 2 Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress. Typeset by David Gregson Associates, Beccles, Suolk Printed in Great Britain by Biddles Ltd, Guildford, Surrey Contents List of contributors ix Preface xv 1 Adaptive internal model control 1 1.1 Introduction 1 1.2 Internal model control (IMC) schemes: known parameters 2 1.3 Adaptive internal model control schemes 7 1.4 Stability and robustness analysis 12 1.5 Simulation examples 18 1.6 Concluding remarks 19 References 21 2 An algorithm for robust adaptive control with less prior knowledge 23 2.1 Introduction 23 2.2 Problem formulation 25 2.3 Ordinary direct adaptive control with dead zone 27 2.4 New robust direct adaptive control 28 2.5 Robust adaptive control with least prior knowledge 32 2.6 Simulation example 36 2.7 Conclusions 38 References 38 3 Adaptive variable structure control 41 3.1 Introduction 41 3.2 Problem formulation 43 3.3 The case ofrelative degree one 46 3.4 The case ofarbitrary relative degree 49 3.5 Computer simulations 56 3.6 Conclusion 59 Appendix 60 References 61 4 Indirect adaptive periodic control 63 4.1 Introduction 63 4.2 Problem formulation 65 4.3 Adaptive control scheme 68 4.4 Adaptive control law 69 4.5 Simulations 74 4.6 Conclusions 78 References 78 5Adaptive stabilization of uncertain discrete-time systems via switching control: the method of localization 80 5.1 Introduction 80 5.2 Problem statement 86 5.3 Direct localization principle 89 5.4 Indirect localization principle 101 5.5 Simulation examples 108 5.6 Conclusions 112 Appendix A 112 Appendix B 115 References 116 6 Adaptive nonlinear control: passivation and small gain techniques 119 6.1 Introduction 119 6.2 Mathematical preliminaries 121 6.3 Adaptive passivation 127 6.4 Small gain-based adaptive control 138 6.5 Conclusions 155 References 156 7 Active identi®cation for control of discrete-time uncertain nonlinear systems 159 7.1 Introduction 160 7.2 Problem formulation 161 7.3 Active identi®cation 166 7.4 Finite duration 178 7.5 Concluding remarks 178 Appendix 181 References 182 vi Contents 8 Optimal adaptive tracking for nonlinear systems 184 8.1 Introduction 184 8.2 Problem statement: adaptive tracking 186 8.3 Adaptive tracking and atclf's 188 8.4 Adaptive backstepping 193 8.5 Inverse optimal adaptive tracking 197 8.6 Inverse optimality via backstepping 202 8.7 Design for strict-feedback systems 205 8.8 Transient performance 209 8.9 Conclusions 210 Appendix A technical lemma 210 References 213 9 Stable adaptive systems in the presence of nonlinear parametrization 215 9.1 Introduction 215 9.2 Statement ofthe problem 218 9.3 Preliminaries 220 9.4 Stable adaptive NP-systems 228 9.5 Applications 236 9.6 Conclusions 245 Appendix Proofs of lemmas 246 References 258 10 Adaptive inverse for actuator compensation 260 10.1 Introduction 260 10.2 Plants with actuator nonlinearities 262 10.3 Parametrized inverses 263 10.4 State feedback designs 265 10.5 Output feedback inverse control 269 10.6 Output feedback designs 271 10.7 Designs for multivariable systems 275 10.8 Designs for nonlinear dynamics 281 10.9 Concluding remarks 284 References 285 11 Stable multi-input multi-output adaptive fuzzy/neural control 287 11.1 Introduction 287 11.2 Direct adaptive control 289 11.3 Indirect adaptive control 296 11.4 Applications 299 11.5 Conclusions 306 References 306 Contents vii 12 Adaptive robust control scheme with an application to PM synchronous motors 308 12.1 Introduction 309 12.2 Problem formulation 310 12.3 Adaptive robust control with -modi®cation 312 12.4 Application to PM synchronous motors 317 12.5 Conclusion 320 Appendix A The derivative of V 1 321 Appendix B The derivative of V 2 322 Appendix C The derivative of V 3 324 Appendix D 325 Appendix E De®nitions of  2 ,  3 , ' 2 ,and' 3 326 Index 000 viii Contents List of contributors Amit Ailon Department ofElectrical and Computer Engineering Ben Gurion University ofthe Negev Israel Anuradha M. Annaswamy Adaptive Control Laboratory Department ofMechanical Engineering Massachusetts Institute ofTechnology Cambridge MA02139 USA Chiang-Ju Chien Department ofElectronic Engineering Hua Fan University Taipei Taiwan ROC Aniruddha Datta Department ofElectrical Engineering Texas A & M University College Station TX 77843±3128, USA