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CHAPTER 1 Introduction 1

1．1 Overview 1

1．2 Conventional Control System Design 3

1．2．1 Mathematical Modeling 3

1．2．2 Performance Objectives and Design Constraints 5

1．2．3 Controller Design 7

1．2．4 Performance Evaluation 8

1．3 Fuzzy Control System Design 9

1．3．1 Modeling Lssues and Performance Objectives 11

1．3．2 Fuzzy Controller Design 12

1．3．3 Performance Evaluation 12

1．3．4 Application Areas 13

1．4 What This Book Is About 14

1．4．1 What the Techniques Are Good For:An Example 14

1．4．2 Objectives of This Book 16

1．5 Summary 16

1．6 For Further Study 17

1．7 Exercises 18

CHAPTER 2 Fuzzy Control:The Basics 21

2．1 Overview 21

2．2 Fuzzy Control: A Tutorial Introduction 22

2．2．1 Choosing Fuzzy Controller Inputs and Outputs 23

2．2．2 Putting Control Knowledge into Rule-Bases 25

2．2．3 Fuzzy Quantification of Knowledge 30

2．2．4 Matching: Determining Which Rules to Use 34

2．2．5 Inference Step:Determining Conclusions 39

2．2．6 Converting Decisions into Actions 41

2．2．7 Graphical Depiction of Fuzzy Decision Making 46

2．2．8 Visualizing the Fuzzy Controller s Dynamical Operation 47

2．3 General Fuzzy Systems 48

2．3．1 Linguistic Variables, Values, and Rules 49

2．3．2 Fuzzy Sets, Fuzzy Logic, and the Rule-Base 52

2．3．3 Fuzzification 57

2．3．4 The Inference Mechanism 58

2．3．5 Defuzzification 61

2．3．6 Mathematical Representations of Fuzzy Systems 65

2．3．7 Takagi-Sugeno Fuzzy Systems 69

2．3．8 Fuzzy Systems Are Universal Approximators 72

2．4 Simple Design Example: The Inverted Pendulum 73

2．4．1 Tuning via Scaling Universes of Discourse 74

2．4．2 Tuning Membership Functions 78

2．4．3 The Nonlinear Surface for the Fuzzy Controller 81

2．4．4 Summary:Basic Design Guidelines 84

2．5 Simulation of Fuzzy Control Systems 85

2．5．1 Simulation of Nonlinear Systems 85

2．5．2 Fuzzy Controller Arrays and Subroutines 88

2．5．3 Fuzzy Controller Pseudocode 89

2．6 Real-Time Implementation Issues 91

2．6．1 Computation Time 91

2．6．2 Memory Requirements 92

2．7 Summary 93

2．8 For Further Study 95

2．9 Exercises 95

2．10 Design Problems 103

CHAPTER 3 Case Studies in Design and Implementation 111

3．1 Overview 111

3．2 Design Methodology 113

3．3 Vibration Damping for a Flexible Robot 115

3．3．1 The Two-Link Flexible Robot 116

3．3．2 Uncoupled Direct Fuzzy Control 120

3．3．3 Coupled Direct Fuzzy Control 124

3．4 Balancing a Rotational Inverted Pendulum 132

3．4．1 The Rotational Inverted Pendulum 132

3．4．2 A Conventional Approach to Balancing Control 135

3．4．3 Fuzzy Control for Balancing 136

3．5 Machine Scheduling 142

3．5．1 Conventional Scheduling Policies 143

3．5．2 Fuzzy Scheduler for a Single Machine 146

3．5．3 Fuzzy Versus Conventional Schedulers 148

3．6 Fuzzy Decision-Making Systems 151

3．6．1 Infectious Disease Warning System 152

3．6．2 Failure Warning System for an Aircraft 155

3．7 Summary 158

3．8 For Further Study 158

3．9 Exercises 159

3．10 Design Problems 161

CHAPTER 4 Nonlinear Analysls 177

4．1 Overview 177

4．2 Parameterized Fuzzy Controllers 179

4．2．1 Proportional Fuzzy Controller 180

4．2．2 Proportional-Derivative Fuzzy Controller 182

4．3 Lyapunov Stability Analysis 183

4．3．1 Mathematical Preliminaries 183

4．3．2 Lyapunov s Direct Method 184

4．3．3 Lyapunov s Indirect Method 185

4．3．4 Example:Inverted Pendulum 186

4．3．5 Example: The Parallel Distributed Compensator 189

4．4 Absolute Stability and the Circle Criterion 193

4．4．1 Analysis of Absolute Stability 193

4．4．2 Example:Temperature Control 197

4．5 Analysis of Steady-State Tracking Error 199

4．5．1 Theory of Tracking Error for Nonlinear Systems 199

4．5．2 Example: Hydrofoil Controller Design 202

4．6 Describing Function Analysis 202

4．6．1 Predicting the Existence and Stability of Llmit Cycles 203

4．6．2 SISO Example: Underwater Vehicle Control System 206

4．6．3 MISO Example: Tape Drive Servo 206

4．7 Limitations of the Theory 208

4．8 Summary 210

4．9 For Further Study 211

4．10 Exercises 212

4．11 Design Problems 215

CHAPTER 5 Fuzzy Identification and Estimation 221

5．1 Overview 221

5．2 Fitting Functions to Data 223

5．2．1 The Function Approximation Problem 223

5．2．2 Relation to Identification, Estimation, and Prediction 226

5．2．3 Choosing the Data Set 227

5．2．4 Incorporating Linguistic Information 228

5．2．5 Case Study: Engine Failure Data Sets 230

5．3 Least Squares Methods 235

5．3．1 Batch Least Squares 235

5．3．2 Recursive Least Squares 239

5．3．3 Tuning Fuzzy Systems 241

5．3．4 Example: Batch Least Squares Training of Fuzzy Systems 244

5．3．5 Example: Recursive Least Squares Training of Fuzzy Systems 245

5．4 Gradient Methods 246

5．4．1 Training Standard Fuzzy Systems 247

5．4．2 Implementation Issues and Example 250

5．4．3 Training Takagi-Sugeno Fuzzy Systems 252

5．4．4 Momentum Term and Step Size 255

5．4．5 Newton and Gauss-Newton Methods 256

5．5 Clustering Methods 259

5．5．1 Clustering with Optimal Output Predefuzzification 259

5．5．2 Nearest Neighborhood Clustering 265

5．6 Extracting Rules from Data 267

5．6．1 Learning from Examples（LFE） 267

5．6．2 Modified Learning from Examples（MLFE） 271

5．7 Hybrid Methods 275

5．8 Case Study: FDI for an Engine 277

5．8．1 Experimental Engine and Testing Conditions 277

5．8．2 Fuzzy Estimator Construction and Results 279

5．8．3 Failure Detection and Identification（FDI）Strategy 281

5．9 Summary 286

1．10 For Further Study 287

5．11 Exercises 287

5．12 Design Problems 295

CHAPTER 6 Adaptive Fuzzy Control 301

6．1 Overview 301

6．2 Fuzzy Model Reference Learning Control（FMRLC） 303

6．2．1 The Fuzzy Controller 305

6．2．2 The Reference Model 308

6．2．3 The Learning Mechanism 309

6．2．4 Alternative Knowledge-Base Modifiers 312

6．2．5 Design Guidelines for the Fuzzy Inverse Model 314

6．3 FMRLC: Design and Implementation Case Studies 316

6．3．1 Cargo Ship Steering 316

6．3．2 Fault-Tolerant Aircraft Control 329

6．3．3 Vibration Damping for a Flexible Robot 339

6．4 Dynamically Focused Learning（DFL） 345

6．4．1 Magnetic Ball Suspension System: Motivation for DFL 346

6．4．2 Auto-Tuning Mechanism 358

6．4．3 Auto-Attentive Mechanism 361

6．4．4 Auto-Attentive Mechanism with Memory 364

6．5 DFL:Design and Implementation Case Studies 368

6．5．1 Rotational Inverted Pendulum 369

6．5．2 Adaptive Machine Scheduling 370

6．6 Indirect Adaptive Fuzzy Control 374

6．6．1 On-Line Identification Methods 374

6．6．2 Adaptive Control for Feedback Linearizable Systems 375

6．6．3 Adaptive Parallel Distributed Compensation 377

6．6．4 Example: Level Control in a Surge Tank 378

6．7 Summary 382

6．8 For Further Study 384

6．9 Exercises 385

6．10 Design Problems 387

CHAPTER 7 Fuzzy Supervlsory Control 391

7．1 Overview 391

7．2 Supervision of Conventional Controllers 393

7．2．1 Fuzzy Tuning of PID Controllers 393

7．2．2 Fuzzy Gain Scheduling 395

7．2．3 Fuzzy Supervision of Conventional Controllers 398

7．3 Supervision of Fuzzy Controllers 399

7．3．1 Rule-Base Supervision 399

7．3．2 Case Study: Vibration Damping for a Flexible Robot 400

7．3．3 Supervised Fuzzy Learning Control 404

7．3．4 Case Study: Fault-Tolerant Aircraft Control 405

7．4 Summary 412

7．5 For Further Study 413

7．6 Design Problems 413

CHAPTER 8 Perspectives on Fuzzy Control 415

8．1 Overview 415

8．2 Fuzzy Versus Conventional Control 416

8．2．1 Modeling Issues and Design Methodology 416

8．2．2 Stability and Performance Analysis 418

8．2．3 Implementation and General Issues 419

8．3 Neural Networks 419

8．3．1 Multilayer Perceptrons 420

8．3．2 Radial Basis Function Neural Networks 423

8．3．3 Relationships Between Fuzzy Systems and Neural Networks 424

8．4 Genetic Algorithms 426

8．4．1 Genetic Algorithms: A Tutorial 427

8．4．2 Genetic Algorithms for Fuzzy System Design and Tuning 433

8．5 Knowledge-Based Systems 436

8．5．1 Expert Control 436

8．5．2 Planning Systems for Control 437

8．6 Intelligent and Autonomous Control 438

8．6．1 What Is Intelligent Control ? 439

8．6．2 Architecture and Characteristics 440

8．6．3 Autonomy 441

8．6．4 Example: Intelligent Vehicle and Highway Systems 442

8．7 Summary 445

8．8 For Further Study 446

8．9 Exercises 446

BIBLIOGRAPHY 451

INDEX 468