Fuzzy System Identification and Adaptive Control (Communications and Control Engineering)

This book provides readers with a systematic and unified framework for identification and adaptive control of Takagi–Sugeno (T–S) fuzzy systems. Its design techniques help readers applying these powerful tools to solve challenging nonlinear control problems. The book embodies a systematic study of fuzzy system identification and control problems, using T–S fuzzy system tools for both function approximation and feedback control of nonlinear systems. Alongside this framework, the book also: * introduces basic concepts of fuzzy sets, logic and inference system; * discusses important properties of T–S fuzzy systems; * develops offline and online identification algorithms for T–S fuzzy systems; * investigates the various controller structures and corresponding design conditions for adaptive control of continuous-time T–S fuzzy systems; * develops adaptive control algorithms for discrete-time input–output form T–S fuzzy systems with much relaxed design conditions, and discrete-time state-space T–S fuzzy systems; and * designs stable parameter-adaptation algorithms for both linearly and nonlinearly parameterized T–S fuzzy systems. The authors address adaptive fault compensation problems for T–S fuzzy systems subject to actuator faults. They cover a broad spectrum of related technical topics and to develop a substantial set of adaptive nonlinear system control tools. __Fuzzy System Identification and Adaptive Control__ helps engineers in the mechanical, electrical and aerospace fields, to solve complex control design problems. The book can be used as a reference for researchers and academics in nonlinear, intelligent, adaptive and fault-tolerant control. Preface 7 Contents 12 1 Introduction 17 1.1 Basic Concepts of Fuzzy Systems 17 1.1.1 Fuzzy Sets 17 1.1.2 Fuzzy Logic Operations 19 1.1.3 Fuzzy Inference System 22 1.2 Typical Fuzzy Systems 26 1.2.1 Mamdani Fuzzy Systems 27 1.2.2 Takagi–Sugeno (T–S) Fuzzy Systems 28 1.3 Fuzzy System Identification 29 1.4 Fuzzy System Based Adaptive Control 31 1.4.1 Fuzzy Systems as Static Function Approximators 32 1.4.2 Fuzzy Systems as Dynamic Systems 33 1.5 What This Book Is About 34 References 35 2 T–S Fuzzy Systems 41 2.1 Static T–S Fuzzy Systems 41 2.2 Dynamic T–S Fuzzy Systems 45 2.2.1 Continuous-Time State-Space Form 45 2.2.2 Discrete-Time State-Space Form 48 2.2.3 Discrete-Time Input–Output Form 49 2.3 Universal Approximation Property 50 2.4 Stability and Stabilization Control 52 2.4.1 Stability of T–S Fuzzy Systems 52 2.4.2 Stabilization Control of T–S Fuzzy Systems 58 2.5 Tracking Control of T–S Fuzzy Systems 60 2.5.1 State Tracking Control 61 2.5.2 Output Tracking Control 63 2.6 Summary 68 References 69 3 Adaptive Control: A Tutorial Introduction 71 3.1 Adaptive Linear Control 72 3.1.1 Indirect Adaptive Control 72 3.1.2 Direct Adaptive Control 75 3.1.3 Model Reference Adaptive Control 77 3.1.4 Discrete-Time Adaptive Linear Control 80 3.2 Adaptive Nonlinear Control 85 3.2.1 A Continuous-Time Design Example 85 3.2.2 A Discrete-Time Design Example 87 3.3 Summary 89 References 90 4 T–S Fuzzy System Identification Using I/O Data 91 4.1 Introduction 91 4.2 Offline Identification of T–S Fuzzy Systems 92 4.2.1 Identification of Premise Variables 93 4.2.2 Identification of Number of Rules 99 4.2.3 Estimation of Consequent Parameters 102 4.2.4 Adjustment of Membership Parameters 103 4.2.5 Procedure for Offline Identification 106 4.2.6 Simulation Study 107 4.3 Online Identification of T–S Fuzzy Systems 109 4.3.1 Online Fuzzy Clustering Algorithm 110 4.3.2 Estimation of Consequent Parameters 112 4.3.3 Procedure for Online Identification 113 4.3.4 Simulation Study 113 4.4 Summary 116 References 119 5 Adaptive T–S Fuzzy State Tracking Control Using State Feedback 120 5.1 Problem Statement 120 5.2 Design for T–S Fuzzy Systems in Canonical Form 121 5.2.1 Plant Model and Reference System 122 5.2.2 Nominal Controller and Matching Conditions 122 5.2.3 Adaptive Control Scheme 125 5.3 Design for T–S Fuzzy Systems in General Form (m leqn) 128 5.3.1 Plant Model and Reference System 128 5.3.2 Nominal Controller and Matching Conditions 129 5.3.3 Adaptive Control Scheme 131 5.4 Design for T–S Fuzzy Systems in General Form (m=n) 136 5.4.1 Nominal Controller and Matching Conditions 137 5.4.2 Adaptive Control Scheme 138 5.4.3 Adaptive Control Design: Special Cases 140 5.5 Simulation Study 147 5.5.1 Simulation System 147 5.5.2 Simulation Results 149 5.6 Summary 152 References 153 6 Adaptive T–S Fuzzy Output Tracking Control Using State Feedback 154 6.1 Problem Statement 155 6.2 Modeling of T–S Fuzzy Systems with Relative Degree and Causality 156 6.2.1 Relative Degree of a Dynamic System 156 6.2.2 Relative Degree of T–S Fuzzy System 158 6.3 Designs for T–S Fuzzy Systems with Relative Degree ρ=1 162 6.3.1 Nominal Controller 163 6.3.2 Adaptive Control Design 164 6.4 Designs for T–S Fuzzy Systems with Relative Degree ρ1 165 6.4.1 Nominal Control Law 165 6.4.2 Adaptive Control Design 166 6.4.3 Stability and Tracking Properties 167 6.5 Simulation Study 171 6.5.1 Simulation System 171 6.5.2 Simulation Results 173 6.6 Summary 176 References 177 7 Adaptive T–S Fuzzy Control Using Output Feedback: SISO Cases 178 7.1 Problem Statement 179 7.2 Approach I: Design Based on Linear Prediction Models 180 7.2.1 T–S Fuzzy Prediction Model via Linear Prediction 181 7.2.2 Nominal Controller 185 7.2.3 Adaptive Control Scheme 186 7.2.4 Simulation Study 191 7.3 Approach II: Design Based on Nonlinear Prediction Model 194 7.3.1 T–S Fuzzy Prediction Model via Nonlinear Prediction 195 7.3.2 Adaptive Predictor 198 7.3.3 Adaptive Control Scheme 202 7.3.4 Simulation Study 205 7.4 Summary 209 References 209 8 Adaptive T–S Fuzzy Control Using Output Feedback: MIMO Case 211 8.1 Problem Statement 212 8.2 MIMO T–S Fuzzy System Prediction Model 213 8.2.1 Interactor Matrix 213 8.2.2 Prediction Model 214 8.2.3 Minimum Phase Property 217 8.3 Adaptive Control Design and Analysis 219 8.3.1 Nominal Controller 220 8.3.2 Parameter Estimation 220 8.3.3 Nonsingularity of sumi=1Nμi i0(t) 222 8.3.4 Adaptive Control Scheme 226 8.4 Simulation Study 229 8.4.1 Simulation System 229 8.4.2 Simulation Results 231 8.5 Summary 235 References 235 9 Adaptive T–S Fuzzy Control with Unknown Membership Functions 236 9.1 Problem Statement 237 9.2 Parameter Estimation Algorithm 238 9.2.1 Nonlinearly Parameterized Model 238 9.2.2 Estimation Error Model 239 9.2.3 Adaptive Law 241 9.2.4 Stability Analysis 242 9.3 Adaptive Control Design 245 9.3.1 Nominal Controller 245 9.3.2 Adaptive Control Scheme 247 9.4 Simulation Study 252 9.4.1 Simulation System 252 9.4.2 Simulation Results 254 9.5 Summary 259 References 259 10 Adaptive Control of T–S Fuzzy Systems with Actuator Faults 260 10.1 Systems with Actuator Faults 261 10.2 Adaptive Fault Compensation Control Using State Feedback 262 10.2.1 Problem Statement 262 10.2.2 Nominal Controller 263 10.2.3 Adaptive Control Scheme 268 10.2.4 Simulation Study 272 10.3 Adaptive Fault Compensation Control Using Output Feedback 273 10.3.1 Problem Statement 274 10.3.2 Nominal Control Design 276 10.3.3 Adaptive Control Scheme 278 10.3.4 Simulation Study 282 10.4 Summary 285 10.5 Concluding Remarks 285 References 286 A Proof of Lemma 8.1 287 Index 290 Front Matter ....Pages i-xvii Introduction (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 1-24 T–S Fuzzy Systems (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 25-54 Adaptive Control: A Tutorial Introduction (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 55-74 T–S Fuzzy System Identification Using I/O Data (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 75-103 Adaptive T–S Fuzzy State Tracking Control Using State Feedback (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 105-138 Adaptive T–S Fuzzy Output Tracking Control Using State Feedback (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 139-162 Adaptive T–S Fuzzy Control Using Output Feedback: SISO Cases (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 163-195 Adaptive T–S Fuzzy Control Using Output Feedback: MIMO Case (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 197-221 Adaptive T–S Fuzzy Control with Unknown Membership Functions (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 223-246 Adaptive Control of T–S Fuzzy Systems with Actuator Faults (Ruiyun Qi, Gang Tao, Bin Jiang)....Pages 247-273 Back Matter ....Pages 275-282