PREFACE ........................................................ xi
CHAPTER 1 INTRODUCTION ......................................... 1
1.1 Fuzzy Systems .............................................. 1
1.2 Expert Knowledge ........................................... 3
1.3 When and When Not to Use Fuzzy Control ..................... 3
1.4 Control .................................................... 4
1.5 Interconnection of Several Subsystems ...................... 6
1.6 Identification and Adaptive Control ........................ 8
1.7 Summary .................................................... 9
Exercises ................................................. 10
CHAPTER 2 BASIC CONCEPTS OF FUZZY SETS ........................ 11
2.1 Fuzzy Sets ................................................ 11
2.2 Useful Concepts for Fuzzy Sets ............................ 15
2.3 Some Set Theoretic and Logical Operations on Fuzzy Sets ... 16
2.4 Example ................................................... 18
2.5 Singleton Fuzzy Sets ...................................... 22
2.6 Summary ................................................... 23
Exercises ................................................. 24
CHAPTER 3 MAMDANI FUZZY SYSTEMS ............................... 27
3.1 If-Then Rules and Rule Base ............................... 27
3.2 Fuzzy Systems ............................................. 29
3.3 Fuzzification ............................................. 29
3.4 Inference ................................................. 30
3.5 Defuzzification ........................................... 30
3.6 Example: Fuzzy System for Wind Chill ...................... 31
3.7 Summary ................................................... 42
Exercises ................................................. 43
CHAPTER 4 FUZZY CONTROL WITH MAMDANI SYSTEMS .................. 46
4.1 Tracking Control with a Mamdani Fuzzy Cascade
Compensator ............................................... 46
4.2 Tuning for Improved Performance by Adjusting Scaling
Gains ..................................................... 53
4.3 Effect of Input Membership Function Shapes ................ 56
4.4 Conversion of PID Controllers into Fuzzy Controllers ...... 59
4.5 Incremental Fuzzy Control ................................. 66
4.6 Summary ................................................... 69
Exercises ................................................. 69
CHAPTER 5 MODELING AND CONTROL METHODS USEFUL FOR FUZZY
CONTROL ............................................. 71
5.1 Continuous-Time Model Forms ............................... 71
5.2 Model Forms for Discrete-Time Systems ..................... 75
5.3 Some Conventional Control Methods Useful in Fuzzy
Control ................................................... 78
5.4 Summary ................................................... 85
Exercises ................................................. 86
CHAPTER 6 TAKAGI-SUGENO FUZZY SYSTEMS ......................... 88
6.1 Takagi-Sugeno Fuzzy Systems as Interpolators between
Memoryless Functions ...................................... 88
6.2 Takagi-Sugeno Fuzzy Systems as Interpolators between
Continuous-Time Linear State-Space Dynamic Systems ........ 92
6.3 Takagi-Sugeno Fuzzy Systems as Interpolators between
Discrete-Time Linear State-Space Dynamic Systems .......... 95
6.4 Takagi-Sugeno Fuzzy Systems as Interpolators between
Discrete-Time Dynamic Systems described by Input-Output
Difference Equations ...................................... 98
6.5 Summary .................................................. 101
Exercises ................................................ 101
CHAPTER 7 PARALLEL DISTRIBUTED CONTROL WITH TAKAGI-SUGENO
FUZZY SYSTEMS ...................................... 106
7.1 Continuous-Time Systems .................................. 106
7.2 Discrete-Time Systems .................................... 109
7.3 Parallel Distributed Tracking Control .................... 112
7.4 Parallel Distributed Model Reference Control ............. 116
7.5 Summary .................................................. 118
Exercises ................................................ 119
CHAPTER 8 ESTIMATION OF STATIC NONLINEAR FUNCTIONS FROM
DATA ............................................... 121
8.1 Least-Squares Estimation ................................. 121
8.2 Batch Least-Squares Fuzzy Estimation in Mamdani Form ..... 124
8.3 Recursive Least-Squares Fuzzy Estimation in Mamdani
Form ..................................................... 132
8.4 Least-Squares Fuzzy Estimation in Takagi-Sugeno Form ..... 135
8.5 Gradient Fuzzy Estimation in Mamdani Form ................ 136
8.6 Gradient Fuzzy Estimation in Takagi-Sugeno Form .......... 145
8.7 Summary .................................................. 146
Exercises ................................................ 147
CHAPTER 9 MODELING OF DYNAMIC PLANTS AS FUZZY SYSTEMS ........ 149
9.1 Modeling Known Plants as Takagi-Sugeno Fuzzy Systems ..... 149
9.2 Identification in Input-Output Difference Equation
Form ..................................................... 154
Form ..................................................... 159
9.3 Identification in Companion Form ......................... 163
9.4 Summary .................................................. 167
Exercises ................................................ 168
CHAPTER 10 ADAPTIVE FUZZY CONTROL ............................. 169
10.1 Direct Adaptive Fuzzy Tracking Control ................... 170
10.2 Direct Adaptive Fuzzy Model Reference Control ............ 173
10.3 Indirect Adaptive Fuzzy Tracking Control ................. 175
10.4 Indirect Adaptive Fuzzy Model Reference Control .......... 179
10.5 Adaptive Feedback Linearization Control .................. 184
10.6 Summary .................................................. 187
Exercises ................................................ 188
REFERENCES .................................................... 190
APPENDIX COMPUTER PROGRAMS .................................... 192
INDEX ......................................................... 229
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