Fuzzy modeling and fuzzy control

Cover......Page 1
Series Information......Page 3
Title Page......Page 4
Publication Data\r......Page 5
Contents......Page 7
Preface......Page 11
1. Fuzzy Set Theory and Rough Set Theory......Page 15
1.1.1 Basic Concepts and Notation......Page 16
1.1.3 Basic Properties of Classical Set Operations......Page 17
1.2.1 Fundamental Concepts of Fuzzy Set Theory......Page 18
1.2.2 Membership Functions......Page 21
1.2.3 Fuzzy Relations......Page 24
1.2.4 Projections and Cylindric Extensions......Page 25
1.2.6 The Extension Principle......Page 27
1.2.7 Basic Concept of Fuzzy Systems......Page 28
1.2.8 Fuzzy Logic and Fuzzy Reasoning......Page 30
1.2.9 Arithmetic Operations on Fuzzy Sets......Page 39
1.3 Rough Set Theory......Page 40
Bibliography......Page 45
2.1 Introduction......Page 47
2.2 Description of the T-S Fuzzy Model......Page 48
2.3.1 Consequent Parameter Identification......Page 51
2.3.2 Premise Parameter Identification......Page 53
2.3.3 Premise Structure Identification......Page 57
2.4.1 The Second T^pe of Fuzzy Model......Page 76
2.4.2 Premise Parameter Identification......Page 77
2.4.3 Consequent Structure and Parameter Identification......Page 81
2.5.1 Approximation Analysis......Page 82
2.5.2 Parameter Identification Algorithm Based on the GA......Page 87
Bibliography......Page 89
3.1 Introduction......Page 91
3.2.1 Rough Set Data Analysis......Page 92
3.2.2 Data Filtering......Page 95
3.2.3 Fuzzy C-Means Clustering Algorithm......Page 97
3.3.1 Problem Description......Page 99
3.3.2 Rough Information Measures......Page 101
3.3.3 Identification Algorithm......Page 103
3.3.5 Numerical Examples......Page 105
3.4.1 Preliminaries......Page 108
3.4.2 Fuzzy Model Identification......Page 109
3.4.3 Simulation......Page 111
3.5.1 Problem Definition......Page 115
3.5.2 Matching Degree and Fitting Degree......Page 116
3.5.3 Modeling Procedure......Page 117
3.5.4 Simulation......Page 118
Bibliography......Page 120
4.1 Introduction......Page 122
4.2.1 Definition of the Fuzzy Hyperbolic Model......Page 123
4.2.3 Neural Network Implementation of the FHM......Page 126
4.2.4 Modeling Process......Page 127
4.3.1 Definition of the Generalized Fuzzy Hyperbolic Model......Page 131
4.3.3 Approximation Capability of the GFHM......Page 134
4.3.4 Identification of the GFHM......Page 137
4.3.5 Numerical Examples......Page 140
Bibliography......Page 147
5.2.1 Fuzzy Logic Control......Page 149
5.2.2 Architecture of a Simple Fuzzy Control System......Page 150
5.2.3 Fuzzification of Information......Page 151
5.2.4 Fuzzy Inference......Page 154
5.2.5 Defuzzification......Page 156
5.3.1 Influence of EK\r......Page 157
5.3.3 Influence of UK......Page 158
5.4 Fuzzy Self-Tuning Control......Page 160
5.4.1 Membership Functions of a Group of Fuzzy Subsets......Page 161
5.4.2 Rough Tuning Mode of FSTCS......Page 164
5.4.3 Precise Tuning Mode of FSTCS......Page 165
5.5 Simulation Comparison Under Disturbances......Page 166
5.5.2 Performance Comparison with Disturbance I......Page 169
5.5.3 Performance Comparison with Disturbances I and II......Page 170
5.7 Automatic Generation of a Fuzzy State-Action Table......Page 171
Bibliography......Page 183
6.1 Introduction......Page 185
6.2 Historical Overview and Problem Description......Page 186
6.3.1 Similarity Measures......Page 187
6.3.2 Knowledge Representation and Pattern Matching......Page 188
6.3.3 Modification Function (McF)......Page 191
6.4 The Function Cf and the Overall Point-Valued THFDP Algorithm......Page 192
6.5.2 \"AND\'\' Composition......Page 194
6.6 Numerical Examples......Page 195
6.7 Fuzzy Control Methods Involving Two Kinds of Uncertainties......Page 197
Bibliography......Page 204
7.1 Introduction......Page 207
7.2 Fundamentals of a Fuzzy Control Scheme via FPE......Page 208
7.3.1 Problem Formulation......Page 209
7.3.2 Preliminaries and Notation......Page 210
7.3.3 Design of an Adaptive Fuzzy H-inf Performance Evaluator......Page 212
7.3.4 Adaptive Fuzzy Controller Design......Page 215
7.3.5 Simulation......Page 217
7.4 Fuzzy State Feedback Control Scheme via FPE......Page 222
7.4.1 Problem Formulation......Page 223
7.4.2 Design of a Fuzzy Performance Evaluator......Page 224
7.4.3 Fuzzy Controller Design......Page 227
7.4.3 Simulation......Page 230
7.5.1 Problem Formulation......Page 236
7.5.2 Design of the Fuzzy Performance Evaluator......Page 238
7.5.3 Fuzzy Controller Design......Page 242
7.5.4 Simulation......Page 245
Bibliography......Page 251
8.1 Introduction......Page 253
8.2.1 The CARIMA Plant Model......Page 254
8.2.2 The Composition of Multivariable Fuzzy Generalized Predictive Control......Page 255
8.3 Equivalent Transformation of the Fuzzy Model......Page 256
8.4 Predictive Control Law for Multivariable Processes......Page 261
8.5 Stability of a Fuzzy Generalized Predictive Control System......Page 263
8.6.1 Closed-Loop Feedback Configuration of Multivariable Fuzzy Model-Based Generalized Predictive Control......Page 265
8.7 Fuzzy Generalized Predictive Control of a Boiler-Turbine Unit......Page 267
8.8.2 Performance Comparison of the System Under Constant Value Perturbation......Page 271
8.9.1 Increasing the Plant\'s Inertia......Page 273
8.9.2 Decreasing the Plant\'s Inertia......Page 274
8.10 Fuzzy Modeling of Operators\' Control Rules with Application......Page 275
8.10.1 The Control of Boiler-Turbine Unit System Based on a Control Function Model......Page 276
8.10.2 Simulation Studies......Page 280
8.11 Summary......Page 281
Bibliography......Page 282
9.1 Introduction......Page 284
9.2.2 Preliminaries......Page 285
9.3.1 Problem Formulation and State Transformation......Page 289
9.3.2 Fuzzy System Formation......Page 292
9.3.3 Robust Controller Design......Page 298
9.4.1 Problem Formulation and State Transformation......Page 300
9.4.3 Robust Controller Design......Page 302
9.5 Numerical Example......Page 303
Bibliography......Page 307
10.1 Introduction......Page 309
10.2 Stable Controller Design by Pole-Placement Method......Page 310
10.3 Nonlinear H-2 Optimal Controller Design......Page 315
10.4 H-inf Controller Design......Page 319
10.5.2 Fuzzy Hyperbolic Guaranteed Cost Controller......Page 322
10.5.3 Simulation Example......Page 328
Bibliography......Page 329
11.1 Introduction......Page 332
11.2 Modeling of a Class of Nonlinear Discrete-Time Systems with Time-Delays Using the T-S Fuzzy System......Page 333
11.3 Fuzzy H-inf Filtering Analysis Based on the T-S Fuzzy Model......Page 337
11.4 Fuzzy H-inf Filter Design......Page 349
11.5 Simulation Example......Page 355
Bibliography......Page 362
12.1 Introduction......Page 365
12.2.1 Preliminaries......Page 366
12.2.2 Stabilization of the Fuzzy Hyperbolic Model......Page 367
12.2.3 Chaotification of the Closed-Loop Fuzzy Hyperbolic......Page 368
12.2.3 Simulation Results......Page 371
12.3.1 Problem Formulation......Page 375
12.3.2 Controller Design......Page 377
12.3.3 Simulation Results......Page 381
12.4 Chaotification of the Original System......Page 385
12.4.1 Impulsive Control Method......Page 388
12.4.2 Inverse Optimal Control Method......Page 389
Bibliography......Page 393
13.1 Introduction......Page 396
13.2 Problem Formation......Page 397
13.3 System Description and Assumptions......Page 399
13.4.1 Single-Input FSMC Technique......Page 400
13.4.2 Stability Analysis of FSMC......Page 405
13.5 Adaptive Feedforward Controller Design in theFourier Space......Page 407
13.6 Convergence Conditions of the Global Closed-Loop System......Page 411
13.7.1 Load System......Page 413
13.7.2 Nonlinear Numerical Example......Page 416
13.8 Summary......Page 418
Bibliography......Page 419
Index......Page 420