John wiley sons stable adaptive control estimation for nonlinear systems neural fuzzy (scanned ocr)

Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques Jeffrey T Spooner, Manfredi Maggiore, Ra´ul Ord´on˜ ez, Kevin M Passino Copyright  2002 John Wiley & Sons, Inc ISBNs: 0-471-41546-4 (Hardback); 0-471-22113-9 (Electronic) STABLE ADAPTIVE CONTROL AND ESTIMATION FOR NONLINEAR SYSTEMS Adaptive and Learning Systems for Signal Processing, Communications, and Control Editor: Simon Haykin Beckerman / ADAPTIVE COOPERATIVE SYSTEMS Chen and Gu / CONTROL-ORIENTED SYSTEM IDENTIFICATION: An tiX Approach Cherkassky Methods and Mulier / LEARNING FROM DATA: Concepts,Theory, Diamantaras and Kung / PRINCIPAL COMPONENT Theory and Applications NEURAL NETWORKS: Haykin / UNSUPERVISED ADAPTIVE FILTERING: Blind Source Separation Haykin / UNSUPERVISED ADAPTIVE FILTERING: Blind Deconvolution Haykin and Puthussarypady Hrycej / NEUROCONTROL: Hyvarinen, Karhunen, Kristic, Kanellakopoulos, CONTROL DESIGN Mann and / CHAOTIC DYNAMICS OF SEA CLUTTER Towards an Industrial Control Methodology and Oja / INDEPENDENT COMPONENT and Kokotovic ANALYSIS / NONLINEAR AND ADAPTIVE / INTELLIGENT IMAGE PROCESSING Nikias and Shao / SIGNAL PROCESSING WITH ALPHA-STABLE DISTRIBUTIONS AND APPLICATIONS Passino and Burgess / STABILITY ANALYSIS OF DISCRETE EVENT SYSTEMS Sanchez-Pena and Sznaier / ROBUST SYSTEMS THEORY AND APPLICATIONS Sandberg, Lo, Fancourt, Principe, Katagiri, and Haykin / NONLINEAR DYNAMICAL SYSTEMS: Feedforward Neural Network Perspectives Spooner, Maggiore, Ordonez, and Passino / STABLE ADAPTIVE CONTROL AND ESTIMATION FOR NONLINEAR SYSTEMS: Neural and Fuzzy Approximator Techniques Tao and Kokotovic / ADAPTIVE CONTROL OF SYSTEMS WITH ACTUATOR AND SENSOR NONLINEARITIES Tsoukalas and Uhrig / FUZZY AND NEURAL APPROACHES IN ENGINEERING Van Hulle / FAITHFUL REPRESENTATIONS AND TOPOGRAPHIC Distortion- to Information-Based Self-Organization Vapnik MAPS: From / STATISTICAL LEARNING THEORY Werbos / THE ROOTS OF BACKPROPAGATION: Neural Networks and Political Forecasting Yee and Haykin and Applications From Ordered Derivatives to / REGULARIZED RADIAL BIAS FUNCTION NETWORKS: Theory STABLE ADAPTIVE CONTROL AND ESTIMATION FOR NONLINEAR SYSTEMS Neural and Fuzzy Approximator Techniques Jeffrey T Spooner Sandia National Laboratories Manfredi Maggiore University of Toronto RaGI Ordbfiez University of Dayton Kevin M Passino The Ohio State University INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Designations used by companies to distinguish their products are often claimed as trademarks In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or ALL CAPITAL LETTERS Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration Copyright  2002 by John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold with the understanding that the publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional person should be sought ISBN 0-471-22113-9 This title is also available in print as ISBN 0-471-41546-4 For more information about Wiley products, visit our web site at www.Wiley.com To our families Contents xv Preface 1 Introduction 1.1 1.2 1.3 Overview Stability and Robustness Adaptive Control: Techniques and Properties 1.3.1 Indirect Adaptive Control Schemes 1.3.2 Direct Adaptive Control Schemes 1.4 The Role of Neural Networks and Fuzzy Systems 1.4.1 Approximator Structures and Properties 1.4.2 Benefits for Use in Adaptive Systems 1.5 Summary I 11 Foundations Mathematical 2.1 2.2 2.3 2.4 4 6 10 Foundations Overview Vectors, Matrices, and Signals: Norms and Properties 2.2.1 Vectors 2.2.2 Matrices 2.2.3 Signals Functions: Continuity and Convergence 2.3.1 Continuity and Differentiation 2.3.2 Convergence Characterizations of Stability and Boundedness 2.4.1 Stability Definitions 13 13 13 14 15 19 21 21 23 24 26 vii CONTENTS VIII 2.5 2.6 2.7 2.8 2.9 Neural 3.1 3.2 3.3 3.4 3.5 2.4.2 Boundedness Definitions Lyapunov’s Direct Method 2.5.1 Preliminaries: Function Properties 2.5.2 Conditions for Stability 2.5.3 Conditions for Boundedness Input-to-State Stability 2.6.1 Input-to-State Stability Definitions 2.6.2 Conditions for Input-to-State Stability Special Classes of Systems 2.7.1 Autonomous Systems 2.7.2 Linear Time-Invariant Systems Summary Exercises and Design Problems Networks 4.4 Fuzzy Systems Overview Neural Networks 3.2.1 Neuron Input Mappings 3.2.2 Neuron Activation Functions 3.2.3 The Mulitlayer Perceptron 3.2.4 Radial Basis Neural Network 3.2.5 Tapped Delay Neural Network Fuzzy Systems 3.3.1 Rule-Base and Fuzzification 3.3.2 Inference and Defuzzification 3.3.3 Takagi-Sugeno Fuzzy Systems Summary Exercises and Design Problems 49 49 50 52 54 57 58 59 60 61 64 67 69 69 73 73 Overview 74 Problem Formulation 76 Linear Least Squares 77 4.3.1 Batch Least Squares 80 4.3.2 Recursive Least Squares 84 Nonlinear Least Squares 4.4.1 Gradient Optimization: Single Training Data Pair 85 4.4.2 Gradient Optimization: Multiple Training Data Pa,irs 87 92 4.4.3 Discrete Time Gradient Updates Optimization 4.1 4.2 4.3 and 30 31 32 34 36 38 38 39 41 41 43 45 45 for Training Approximators CONTENTS ix 4.5 4.6 Function 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 II 4.4.4 Constrained Optimization 4.4.5 Line Search and the Conjugate Gradient Method Summary Exercises and Design Problems Approximation Overview Function Approximation 5.2.1 Step Approximation 5.2.2 Piecewise Linear Approximation 5.2.3 Stone-Weierstrass Approximation Bounds on Approximator Size 5.3.1 Step Approximation 5.3.2 Piecewise Linear Approximation Ideal Parameter Set and Representation Error Linear and Nonlinear Approximator Structures 5.5.1 Linear and Nonlinear Parameterizations 5.5.2 Capabilities of Linear vs Nonlinear Approximator: ; 5.5.3 Linearizing an Approximator Discussion: Choosing the Best Approximator Summary Exercises and Design Problems State-Feedback Control 6.1 6.2 6.3 6.4 6.5 of Nonlinear Control Systems Overview The Error System and Lyapunov Candidate 6.2.1 Error Systems 6.2.2 Lyapunov Candidates Canonical System Representations 6.3.1 State-Feedback Linearizable Systems 6.3.2 Input-Output Feedback Linearizable Systems 6.3.3 Strict-Feedback Systems Coping with Uncertainties: Nonlinear Damping 6.4.1 Bounded Uncertainties 6.4.2 Unbounded Uncertainties 6.4.3 What if the Matching Condition Is Not Satisfied? Coping with Partia,l Information: Dynamic Normalization 94 95 101 102 105 105 106 107 113 115 119 119 120 122 123 123 124 126 128 130 130 133 135 135 137 137 140 141 141 149 153 159 160 161 162 163 CONTENTS X 6.6 6.7 6.8 Direct 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Adaptive 8.3 8.4 8.5 Adaptive Control Overview Uncertainties Satisfying Matching Conditions 8.2.1 Static Uncertainties 8.2.2 Dynamic Uncertainties Beyond the Matching Condition 8.3.1 A Second-Order System 8.3.2 Strict-Feedback Systems with Static Uncertainties 8.3.3 Strict-Feedback Systems with Dynamic Uncertainties Summary Exercises and Design Problems Implementations 9.1 9.2 Control Overview Lyapunov Analysis and Adjustable Approximators The Adaptive Controller 7.3.1 o-modification 7.3.2 c-modification Inherent Robustness 7.4.1 Gain Margins 7.4.2 Disturbance Rejection Improving Performance 7.5.1 Proper Initialization 7.5.2 Redefining the Approximator Extension to Nonlinear Parameterization Summary Exercises and Design Problems Indirect 8.1 8.2 Using Approximators in Controllers 6.6.1 Using Known Approximations of System Dynamics 6.6.2 When the Approximator Is Only Valid on a Region Summary Exercises and Design Problems and Comparative Studies Overview Control of Input-Output Feedback Linearizable Systems 9.2.1 Direct Adaptive Control 9.2.2 Indirect Adaptive Control 165 165 167 171 172 179 179 180 184 185 198 201 201 202 203 204 205 206 208 210 215 215 216 216 227 236 236 239 248 254 254 257 257 258 258 261 CONTENTS xi 9.3 9.4 9.5 The Rotational Inverted Pendulum Modeling and Simulation Two Non-Adaptive Controllers 9.5.1 Linear Quadratic Regulator 9.5.2 Feedback Linearizing Controller Adaptive Feedback Linearization 9.6 Indirect Adaptive Fuzzy Control 9.7.1 Design Without Use of Plant Dynamics Knowledge 9.7.2 Incorporation of Plant Dynamics Knowledge 9.8 Direct Adaptive Fuzzy Control 9.8.1 Using Feedback Linearization as a Known Controller 9.8.2 Using the LQR to Obtain Boundedness 9.8.3 Other Approaches 9.9 Summary 9.10 Exercises and Design Problems 9.7 III Output-Feedback 10 Output-Feedback Control Control 10.1 IO.2 10.3 10.4 Overview Partial Information Framework Output-Feedback Systems Separation Principle for Stabilization 10.4.1 Observability and Nonlinear Observers 10.4.2 Peaking Phenomenon 10.4.3 Dynamic Projection of the Observer Estimate 10.4.4 Output-Feedback Stabilizing Controller 10.5 Extension to MIMO Systems 10.6 How to Avoid Adding Integrators 10.7 Coping with Uncertainties 10.8 Output-Feedback Tracking 10.8.1 Practical Internal Models 10.8.2 Separation Principle for Tracking 10.9 Summary lO.lOExercises and Design Problems 11 Adaptive Output Feedback Control 11.1 Overview 11.2 Control of Systems in Adaptive Tracking Form 263 264 266 267 268 271 274 274 282 285 286 290 296 299 300 305 307 307 308 310 317 317 325 327 333 337 339 347 350 353 357 359 360 363 363 364 ... on Intelligent Adaptive Systems Overview Relations to Conventional Adaptive Control Genetic Adaptive Systems Expert Control for Adaptive Systems Planning Systems for Adaptive Control Intelligent... Haykin / NONLINEAR DYNAMICAL SYSTEMS: Feedforward Neural Network Perspectives Spooner, Maggiore, Ordonez, and Passino / STABLE ADAPTIVE CONTROL AND ESTIMATION FOR NONLINEAR SYSTEMS: Neural and Fuzzy. .. Copyright  2002 John Wiley & Sons, Inc ISBNs: 0-471-41546-4 (Hardback); 0-471-22113-9 (Electronic) Part I Foundations Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator