CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS: SYSTEM IDENTIFICATION AND ADAPTIVE CONTROL
1 Introduction 1 11 Basic Concepts of Fuzzy Systems 1 111 Fuzzy Sets 1 112 Fuzzy Logic Operations 3 113 Fuzzy Inference System 6 12 Typical Fuzzy Systems 10 121 Mamdani Fuzzy Systems 11 122 Takagi–Sugeno (T–S) Fuzzy Systems 12 13 Fuzzy System Identification 13 14 Fuzzy System Based Adaptive Control 15 141 Fuzzy Systems as Static Function Approximators 16 142 Fuzzy Systems as Dynamic Systems 17 15 What This Book Is About 18 References 19 2 T–S Fuzzy Systems 25 21 Static T–S Fuzzy Systems 25 22 Dynamic T–S Fuzzy Systems 29 221 Continuous-Time State-Space Form 29 222 Discrete-Time State-Space Form 32 223 Discrete-Time Input–Output Form 33 23 Universal Approximation Property 34 24 Stability and Stabilization Control 36 241 Stability of T–S Fuzzy Systems 36 242 Stabilization Control of T–S Fuzzy Systems 42 25 Tracking Control of T–S Fuzzy Systems 44 251 State Tracking Control 45 252 Output Tracking Control 47 26 Summary 52 References 53 3 Adaptive Control: A Tutorial Introduction 55 31 Adaptive Linear Control 56 311 Indirect Adaptive Control 56 312 Direct Adaptive Control 59 313 Model Reference Adaptive Control 61 314 Discrete-Time Adaptive Linear Control 64 32 Adaptive Nonlinear Control 69 321 A Continuous-Time Design Example 69 322 A Discrete-Time Design Example 71 33 Summary 73 References 74 4 T–S Fuzzy System Identification Using I/O Data 75 41 Introduction 75 42 Offline Identification of T–S Fuzzy Systems 76 421 Identification of Premise Variables 77 422 Identification of Number of Rules 83 423 Estimation of Consequent Parameters 86 424 Adjustment of Membership Parameters 87 425 Procedure for Offline Identification 90 426 Simulation Study 91 43 Online Identification of T–S Fuzzy Systems 93 431 Online Fuzzy Clustering Algorithm 94 432 Estimation of Consequent Parameters 96 433 Procedure for Online Identification 97 434 Simulation Study 97 44 Summary 100 References 103 5 Adaptive T–S Fuzzy State Tracking Control Using State Feedback 105 51 Problem Statement 105 52 Design for T–S Fuzzy Systems in Canonical Form 106 521 Plant Model and Reference System 107 522 Nominal Controller and Matching Conditions 107 523 Adaptive Control Scheme 110 53 Design for T–S Fuzzy Systems in General Form (m n) 113 531 Plant Model and Reference System 113 532 Nominal Controller and Matching Conditions 114 533 Adaptive Control Scheme 116 54 Design for T–S Fuzzy Systems in General Form (m ¼ n) 121 541 Nominal Controller and Matching Conditions 122 542 Adaptive Control Scheme 123 543 Adaptive Control Design: Special Cases 125 55 Simulation Study 132 551 Simulation System 132 552 Simulation Results 134 56 Summary 137 References 138 6 Adaptive T–S Fuzzy Output Tracking Control Using State Feedback 139 61 Problem Statement 140 62 Modeling of T–S Fuzzy Systems with Relative Degree and Causality 141 621 Relative Degree of a Dynamic System 141 622 Relative Degree of T–S Fuzzy System 143 63 Designs for T–S Fuzzy Systems with Relative Degree q ¼ 1 147 631 Nominal Controller 148 632 Adaptive Control Design 149 64 Designs for T–S Fuzzy Systems with Relative Degree q1 150 641 Nominal Control Law 150 642 Adaptive Control Design 151 643 Stability and Tracking Properties 152 65 Simulation Study 156 651 Simulation System 156 652 Simulation Results 158 66 Summary 161 References 162 7 Adaptive T–S Fuzzy Control Using Output Feedback: SISO Cases 163 71 Problem Statement 164 72 Approach I: Design Based on Linear Prediction Models 165 721 T–S Fuzzy Prediction Model via Linear Prediction 166 722 Nominal Controller 170 723 Adaptive Control Scheme 171 724 Simulation Study 176 73 Approach II: Design Based on Nonlinear Prediction Model 179 731 T–S Fuzzy Prediction Model via Nonlinear Prediction 180 732 Adaptive Predictor 183 733 Adaptive Control Scheme 187 734 Simulation Study 190 74 Summary 194 References 194 8 Adaptive T–S Fuzzy Control Using Output Feedback: MIMO Case 197 81 Problem Statement 198 82 MIMO T–S Fuzzy System Prediction Model 199 821 Interactor Matrix 199 822 Prediction Model 200 823 Minimum Phase Property 203 83 Adaptive Control Design and Analysis 205 831 Nominal Controller 206 832 Parameter Estimation 206 833 Nonsingularity of PNi ¼1 li ^bi 0 ðtÞ 208 834 Adaptive Control Scheme 212 84 Simulation Study 215 841 Simulation System 215 842 Simulation Results 217 85 Summary 221 References 221 9 Adaptive T–S Fuzzy Control with Unknown Membership Functions 223 91 Problem Statement 224 92 Parameter Estimation Algorithm 225 921 Nonlinearly Parameterized Model 225 922 Estimation Error Model 226 923 Adaptive Law 228 924 Stability Analysis 229 93 Adaptive Control Design 232 931 Nominal Controller 232 932 Adaptive Control Scheme 234 94 Simulation Study 239 941 Simulation System 239 942 Simulation Results 241 95 Summary 246 References 246 10 Adaptive Control of T–S Fuzzy Systems with Actuator Faults 247 101 Systems with Actuator Faults 248 102 Adaptive Fault Compensation Control Using State Feedback 249 1021 Problem Statement 249 1022 Nominal Controller 250 1023 Adaptive Control Scheme 255 1024 Simulation Study 259 103 Adaptive Fault Compensation Control Using Output Feedback 260 1031 Problem Statement 261 1032 Nominal Control Design 263 1033 Adaptive Control Scheme 265 1034 Simulation Study 269 104 Summary 272 105 Concluding Remarks 272 References 273