Adaptive Control Systems Adaptive Control Systems GANG FENG and ROGELIO LOZANO OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Newnes An imprint of Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801±2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 1999 # Reed Educational and Professional Publishing Ltd 1999 All rights reserved. No part of this 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 of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a 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 of this 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 of relative degree one 46 3.4 The case of arbitrary 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 5 Adaptive 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 of the 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 of Electrical and Computer Engineering Ben Gurion University of the Negev Israel Anuradha M. Annaswamy Adaptive Control Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge MA02139 USA Chiang-Ju Chien Department of Electronic Engineering Hua Fan University Taipei Taiwan ROC Aniruddha Datta Department of Electrical Engineering Texas A & M University College Station TX 77843±3128, USA Dimitrios Dimogianopoulos Universite de Technologie de Compiegne HEUDIASYC UMR 6599 CNRS-UTC BP 20.529 60200 Compiegne France Gang Feng School of Electical Engineering University of New South Wales Sydney, NSW 2052 Australia Li-Chen Fu Department of Computer Science & Information Engineering National Taiwan University Taipei Taiwan ROC Minyue Fu Department of Electrical and Computer Engineering The University of Newcastle NSW 2308 Australia David J. Hill School of Electrical and Information Engineering Bldg J13 Sydney University New South Wales 2006, Australia Qing-Wei Jia Department of Electrical Engineerng National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Y. A. Jiang School of Electrical Engineering University of New South Wales Sydney NSW 2052 USA x List of contributors [...]... reducing a priori knowledge of the systems and improving the transient performance of adaptive control systems Most recently, adaptive control of nonlinear systems has received great attention and a number of signi®cant results have been obtained In this book, we have compiled some of the most recent developments of adaptive control for both linear and nonlinear systems from leading world researchers... contribution in this book is `Adaptive internal model control' by A Datta and L Xing It develops a systematic theory for the design and analysis of adaptive internal model control schemes The ubiquitous certainty equiva- xvi Preface lence principle of adaptive control is used to combine a robust adaptive law with robust internal model controllers to obtain adaptive internal model control schemes which can... class of adaptive controllers for strict-feedback systems These controllers solve a problem left open in the previous adaptive backstepping designs ± getting transient performance bounds that include an estimate of control e€ort The next contribution is `Stable adaptive systems in the presence of nonlinear parameterization' by A M Annaswamy and A P Loh This chapter addresses the problem of adaptive control. .. adaptive law with a robust internal model controller structure The next contribution is `An algorithm for robust direct adaptive control with less prior knowledge' by G Feng, Y A Jiang and R Zmood It discusses several approaches to minimizing a priori knowledge required on the unknown plants for robust adaptive control It takes a discrete time robust direct adaptive control algorithm with a dead zone as... contribution is `Adaptive stabilization of uncertain discrete-time systems via switching control: the method of localization' by P V Zhivoglyadov, R Middleton and M Fu It presents a new systematic switching control approach to adaptive stabilization of uncertain discrete-time systems The approach is based on a method of localization which is conceptually di€erent from supervisory adaptive control schemes... linearly parametrized nonlinear systems with only unknown parameters, the concept of adaptive passivation can be used to unify and extend most of the known adaptive nonlinear control algorithms based on Lyapunov methods A novel recursive robust adaptive control method by means of backstepping and small gain techniques is also developed to generate a new class of adaptive nonlinear controllers with robustness... Preface Adaptive control has been extensively investigated and developed in both theory and application during the past few decades, and it is still a very active research ®eld In the earlier stage, most studies in adaptive control concentrated on linear systems A remarkable development of the adaptive control theory is the resolution of the so-called ideal problem, that is, the proof that several adaptive. .. imposed on the controllers, and convergence of the tracking error to zero is guaranteed The ®nal contribution is `Adaptive robust control scheme with an application to PM synchronous motors' by J X Xu, Q W Jia and T H Lee A new, adaptive, robust control scheme for a class of nonlinear uncertain dynamical systems is presented To reduce the robust control gain and widen the application scope of adaptive techniques,... ubiquitous certainty equivalence principle of adaptive control is used to combine a robust adaptive law with robust internal model controllers to obtain adaptive internal model control schemes which can be proven to be robustly stable Speci®c controller structures considered include those of the model reference, `partial' pole placement, and H2 and HI optimal control types The results here not only provide... straightforward except in the case of adaptive H2 optimal control Accordingly, we ®rst discuss the simpler cases before giving a detailed treatment of the more involved one 14 Adaptive internal model control For the case of adaptive partial pole placement control, the continuity follows trivially from the fact that the IMC parameter is independent of …t† For model reference adaptive control, the continuity is . Adaptive Control Systems Adaptive Control Systems GANG FENG and ROGELIO LOZANO OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Newnes An imprint. Computer Engineering Ben Gurion University of the Negev Israel Anuradha M. Annaswamy Adaptive Control Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge MA02139 USA Chiang-Ju. of the systems and improving the transient performance of adaptive control systems. Most recently, adaptive control of nonlinear systems has received great attention and a number of signi®cant