Fuzzy control : synthesis and analysis

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Chichester : John Wiley, 2000

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9780471986317

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004467605	TJ213 F875 2000	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000004841486	TJ213 F875 2000	Open Access Book	Book	Searching... Unknown

Fuzzy Control Synthesis and Analysis Edited by Shehu S. Farinwata Ford Motor Company, Research Laboratory, Dearborn, Michigan, USA Dimitar Filev Ford Motor Company, AMTDC, Redford, Michigan, USA Reza Langari Texas A & M University, College Station, Texas, USA Fuzzy techniques are used to cope with imprecision in the basic elements of a process under control. Written by an international team of researchers this edited volume covers the modeling, analysis and synthesis of fuzzy control systems. Features include:
? Comprehensive coverage of fuzzy dynamical systems, robustness, stability and sensitivity -- giving the reader a good grasp of the fundamentals of fuzzy control
? Focus on the analytical structures of new fuzzy modeling approaches based on the Takagi-Sugeno-Kang (TSK) or Takagi-Sugeno (TS) model
? Applications of fuzzy control to aircraft systems, rocket engines and automotive engines
? Problems and examples illustrating how fuzzy approaches may be applied to the modeling, analysis and synthesis of closed-loop systems
Design and control engineers will value the advanced control techniques and new design and analysis tools presented. Postgraduates studying fuzzy control will find this book a useful reference on synthesis, systems analysis and advanced nonlinear control methods.

Author Notes

Shehu S. Farinwata and Dimitar P. Filev are the authors of Fuzzy Control: Synthesis and Analysis, published by Wiley.

Editor's Preface	p. xi
List of Contributors	p. xix
About the Editors	p. xxi
Acknowledgments	p. xxiii
Modeling	p. 1
1 Information Granularity in the Analysis and Design of Fuzzy Controllers	p. 3
1.1 Introduction	p. 3
1.2 The Basic Architecture of the Fuzzy Controller and its Non-linear Relationships	p. 4
1.3 Set-Based Approximation of Fuzzy Sets	p. 7
1.4 Information Granularity of the Rules of the Fuzzy Controller	p. 10
1.4.1 Fuzzy Sets and Information Granularity	p. 11
1.5 Robustness Properties of the Fuzzy Controller	p. 13
1.6 Linguistic Information as Inputs of the Fuzzy Controller	p. 17
1.7 Conclusions	p. 21
Acknowledgment	p. 21
References	p. 21
2 Fuzzy Modeling for Predictive Control	p. 23
2.1 Introduction	p. 23
2.2 Fuzzy Modeling	p. 24
2.2.1 Outline of the Modeling Approach	p. 24
2.3 Extraction of an Initial Rule Base	p. 26
2.4 Simplification and Reduction of the Initial Rule Base	p. 27
2.4.1 Similarity Analysis	p. 28
2.4.2 Simplification and Reduction	p. 28
2.5 Model Predictive Control	p. 30
2.5.1 Basic Principles	p. 30
2.5.2 Optimization in MPC	p. 31
2.5.3 The Branch-and-Bound Optimization	p. 32
2.6 Modeling and Control of an HVAC Process	p. 34
2.6.1 Initial Modeling of the System	p. 35
2.6.2 Validating the Initial Model	p. 35
2.6.3 Simplifying the HVAC Model	p. 39
2.6.4 Control Results	p. 40
2.6.5 Summary of Results	p. 41
2.7 Concluding Remarks	p. 42
Appendix A The Gustafson--Kessel Clustering Algorithm	p. 43
Appendix B The Rule Base Simplification Algorithm	p. 44
References	p. 45
3 Adaptive and Learning Schemes for Fuzzy Modeling	p. 47
3.1 Introduction	p. 47
3.2 Identification Problems of the TSK Fuzzy Models	p. 49
3.3 Criteria and Schemes for Learning and Evaluation of Fuzzy Models	p. 54
3.3.1 The Global Learning Criterion, Q[subscript G]	p. 54
3.3.2 The Local Learning Criterion, Q[subscript L]	p. 55
3.3.3 Evaluation Criteria	p. 56
3.4 Algorithms for Global Learning by Fuzzy Models	p. 56
3.4.1 Comparison of the Learning Algorithm Using a Numerical Example	p. 59
3.5 Algorithm for Local Learning by Fuzzy Models	p. 63
3.6 Reinforced Learning Algorithm	p. 66
3.7 Simulation Results for Control Applications	p. 67
3.8 Conclusions	p. 70
References	p. 70
4 Fuzzy System Identification with General Parameter Radial Basis Function Neural Network	p. 73
4.1 Introduction	p. 73
4.2 Fuzzy Systems through Neural Networks	p. 75
4.2.1 Radial Basis Function Neural Networks	p. 77
4.3 General Parameter Radial Basis Function Network (GP RBFN)	p. 78
4.3.1 General Parameter Method for System Identification	p. 79
4.3.2 GP RBFN Training Algorithm	p. 80
4.4 GP RBFN Adaptive Fuzzy Systems (AFSs)	p. 81
4.4.1 Basic Algorithm	p. 81
4.4.2 Unbiasedness Criterion for the GP RBFN AFS	p. 83
4.5 Simulation Results	p. 84
4.6 Conclusion	p. 90
References	p. 91
Analysis	p. 93
5 Lyapunov Stability Analysis of Fuzzy Dynamic Systems	p. 95
5.1 Introduction	p. 95
5.2 Mathematical Preliminaries	p. 96
5.3 Construction of Fuzzy Dynamic Models from Discrete-Time Stochastic Models	p. 97
5.3.1 Construction of Fuzzy Dynamic Models via Fuzzy Composition	p. 98
5.3.2 Construction of a Fuzzy Dynamic Model via the Fuzzy Extension Principle	p. 99
5.4 Stability Analysis of Fuzzy Dynamic Systems	p. 99
5.4.1 Convergence in Fuzzy Dynamic Systems	p. 100
5.4.2 Stability of Fuzzy Dynamic Systems	p. 100
5.4.3 The Direct Lyapunov Method for Fuzzy Dynamic Systems	p. 103
5.5 Application--First-Order Fuzzy Dynamic System	p. 104
5.6 Concluding Remarks	p. 110
References	p. 111
6 Passivity and Stability of Fuzzy Control Systems	p. 113
6.1 Introduction	p. 113
6.2 Fuzzy Control Systems	p. 114
6.2.1 Mamdani Fuzzy Controllers	p. 114
6.2.2 Takagi--Sugeno Fuzzy Control Systems	p. 115
6.3 Stability and Passivity of Fuzzy Controllers	p. 117
6.3.1 Basic Concepts	p. 117
6.3.2 Passivity of QPI Controllers	p. 122
6.3.3 Passivity of DPS Controllers	p. 123
6.3.4 Passivity of Polytopic Differential Inclusions	p. 126
6.4 Stability of Feedback Control with Fuzzy Controllers	p. 130
6.4.1 Feedback Control with QPI Mamdani Controllers	p. 131
6.4.2 Feedback Control with DPS Mamdani Controllers	p. 131
6.4.3 Feedback Control with Linear Takagi--Sugano Controllers	p. 133
6.5 Applications	p. 135
6.5.1 Control of LTI Systems by Fuzzy Controllers	p. 136
6.5.2 Fuzzy Control of Euler--Lagrange Systems	p. 137
6.6 Conclusions	p. 138
Acknowledgments	p. 139
Appendix	p. 139
References	p. 142
7 Frequency Domain Analysis of MIMO Fuzzy Control Systems	p. 145
7.1 Introduction	p. 145
7.2 Multiple Equilibria in MIMO Fuzzy Control Systems	p. 146
7.3 Frequency Analysis of Limit Cycles	p. 148
7.4 Robust Analysis of Limit Cycles using Singular Values	p. 149
7.5 Conclusions	p. 151
Acknowledgments	p. 151
References	p. 151
8 Analytical Study of Structure of a Mamdani Fuzzy Controller with Three Input Variables	p. 153
8.1 Introduction	p. 153
8.2 Configuration of the Fuzzy Controller	p. 154
8.3 Analytical Study of the Fuzzy Controller Structure	p. 157
8.4 Conclusion	p. 162
Acknowledgment	p. 162
References	p. 162
9 An Approach to the Analysis of Robust Stability of Fuzzy Control Systems	p. 165
9.1 Introduction	p. 165
9.2 Perspective	p. 166
9.3 The Nominal Fuzzy Control Problem	p. 167
9.4 Equilibrium Points for Fuzzy Controlled Processes	p. 168
9.5 Fuzzy Robustness Analysis	p. 168
9.5.1 Robustness Problem Statement	p. 169
9.5.2 Concepts of Sensitivity and Robustness	p. 170
9.5.3 Formulation of Fuzzy System Robustness	p. 171
9.5.4 The Main Result	p. 173
9.5.5 Derivation of the Main Result	p. 173
9.6 Generalization of the Robust Stability Result	p. 174
9.6.1 Virtual Interactions Based on Stability	p. 175
9.6.2 General Result for Robust Stabilization	p. 177
9.6.3 Minimizing dV	p. 177
9.7 Fuzzy Extremes of Perturbations	p. 178
9.7.1 A Measure of Fuzzy Robustness	p. 179
9.7.2 Comments	p. 180
9.8 Application Example	p. 182
9.8.1 Problem Statement	p. 185
9.8.2 Simulation Studies and Results	p. 186
9.8.3 Discussion	p. 196
9.9 Conclusions	p. 196
Bibliography	p. 197
10 Fuzzy Control Systems Stability Analysis with Application to Aircraft Systems	p. 203
10.1 Introduction	p. 203
10.1.1 Fuzzy Control	p. 204
10.1.2 Lyapunov Stability of Non-linear Fuzzy Control Systems	p. 205
10.1.3 The Fuzzy Control Problem	p. 205
10.1.4 Equilibrium Points for Fuzzy Controlled Processes	p. 207
10.1.5 The Partitioned State Space	p. 208
10.1.6 Dissipative Mapping and Input-Output Stability	p. 208
10.1.7 Dissipative Mapping for the Fuzzy Control System	p. 210
10.1.8 Stability of Linear Fuzzy Control Systems	p. 211
10.1.9 Positive Realness and Dissipativeness	p. 212
10.1.10 Verifying Dissipativeness	p. 214
10.2 Linear Continuous-Time Model Application	p. 214
10.2.1 A Missile Autopilot	p. 214
10.2.2 Analysis	p. 215
10.2.3 Simulation Studies and Results	p. 219
10.2.4 Conclusions	p. 220
10.3 Linear Discrete-Time Model Application	p. 221
10.3.1 Advanced Technology Wing Aircraft Model	p. 221
10.3.2 Introduction	p. 221
10.3.3 The ATW Problem	p. 222
10.3.4 Control Architecture	p. 223
10.3.5 Control Rule Synthesis	p. 224
10.3.6 Stability Analysis	p. 227
10.3.7 Conclusions	p. 232
10.4 Summary	p. 233
Bibliography	p. 233
Synthesis	p. 237
11 Observer-Based Controller Synthesis for Model-Based Fuzzy Systems via Linear Matrix Inequalities	p. 239
11.1 Introduction	p. 239
11.2 Takagi-Sugano Models	p. 240
11.2.1 Continuous-Time T-S Models	p. 240
11.2.2 Continuous-Time T-S Controllers and Closed-Loop Stability	p. 241
11.2.3 Discrete-Time T-S Controllers	p. 242
11.3 LMI Stability Conditions for T-S Fuzzy Systems	p. 243
11.3.1 The Continuous-Time Case	p. 243
11.3.2 The Discrete-Time Case	p. 243
11.4 Fuzzy Observers	p. 244
11.4.1 Why Output Feedback?	p. 244
11.4.2 Continuous-Time T-S Fuzzy Observers	p. 244
11.4.3 Separation Property of the Observer/Controller	p. 246
11.4.4 Discrete-Time T-S Fuzzy Observers	p. 247
11.5 Numerical Example	p. 249
11.6 Conclusion	p. 252
References	p. 252
12 LMI-Based Fuzzy Control: Fuzzy Regulator and Fuzzy Observer Design via LMIs	p. 253
12.1 Introduction	p. 253
12.2 Takagi-Sugano Fuzzy Model	p. 254
12.3 Fuzzy Regulator Design via LMIs	p. 255
12.3.1 Parallel Distributed Compensation	p. 255
12.3.2 Control Performance Represented by LMIs	p. 256
12.4 Fuzzy Observer Design	p. 262
12.5 Conclusions	p. 263
References	p. 264
13 A framework for the Synthesis of PDC-Type Takagi-Sugano Fuzzy Control Systems: An LMI Approach	p. 267
13.1 Introduction	p. 267
13.1.1 Brief Historical Overview	p. 267
13.2 Background Materials	p. 268
13.2.1 T-S Fuzzy Model of Non-linear Dynamic Systems and its Stability	p. 268
13.2.2 PDC-Type T-S Fuzzy Control System and its Stability	p. 269
13.3 Stability LMIs as a Framework for the Synthesis of PDC-Type T-S Fuzzy Control Systems	p. 271
13.4 Pole Placement Constraint LMIs as Performance Specifications for the Synthesis of PDC-Type T-S Fuzzy Control Systems	p. 274
13.5 An Extension to PDC-Type T-S Fuzzy Control Systems with Parameter Uncertainties	p. 276
13.6 A Simulated Example	p. 279
13.7 Concluding Remarks	p. 281
References	p. 282
14 On Adaptive Fuzzy Logic Control on Non-linear Systems--Synthesis and Analysis	p. 283
14.1 Introduction	p. 283
14.2 Control Objective	p. 284
14.3 DFLS Identifier	p. 285
14.4 Control Law of the System	p. 287
14.5 Adaptive Law for the Parameter Vector Y	p. 288
14.6 Adaptive Law for g	p. 290
14.7 Stability Properties of the DFLS Control Algorithm	p. 291
14.8 Illustrative Application	p. 292
14.9 Concluding Remarks	p. 295
Appendix Proof of Theorem 7.1	p. 296
References	p. 307
15 Stabilization of Direct Adaptive Fuzzy Control Systems: Two Approaches	p. 309
15.1 Introduction	p. 309
15.2 Integral Sliding-Mode Adaptive FLC: Approach I	p. 310
15.2.1 Structure of an Integral Sliding-Mode Adaptive FLC	p. 310
15.2.2 Stabilization of the Integral Sliding-mode Adaptive FLC	p. 311
15.2.3 Properties of the Integral Sliding-Model Adaptive FLC	p. 313
15.3 New Fuzzy Logic Based Learning Control: Approach II	p. 314
15.3.1 Structure of the New Fuzzy Logic Based Learning Control	p. 314
15.3.2 Stabilization of the New Fuzzy Logic Based Learning Control	p. 314
15.3.3 Discussion of the New Fuzzy Logic Based Learning Control	p. 316
15.4 Simulation	p. 316
15.4.1 Approach I	p. 316
15.4.2 Approach II	p. 317
15.5 Concluding Remarks	p. 319
References	p. 320
16 Gain Scheduling Based Control of a Class of TSK Systems	p. 321
16.1 Introduction	p. 321
16.2 TSK Model as a Gain Scheduled System	p. 322
16.3 Stability Conditions for TSK Fuzzy Systems	p. 324
16.4 Synthesis of TSK Compensators	p. 327
16.5 Analytic Form of the Polytopic TSK Compensator	p. 330
16.6 Parameterization of Non-parametric TSK Compensators	p. 333
16.7 Conclusion	p. 334
References	p. 334
17 Output Tracking Using Fuzzy Neural Networks	p. 335
17.1 Introduction	p. 335
17.2 Problem Statement--Assumptions	p. 337
17.3 The Structure of the Controller	p. 339
17.4 The Main Results	p. 340
17.5 The Learning Algorithm	p. 341
17.6 Illustrative Examples	p. 342
17.7 Comprehensive Results and Conclusions	p. 346
References	p. 347
18 Fuzzy Life-Extending Control of Mechanical Systems	p. 349
18.1 Introduction	p. 349
18.2 Architecture of Life-Extending Control Systems	p. 351
18.3 Life-Extending Control of a Rocket Engine	p. 352
18.3.1 Inner Loop Feedback Controller for LECS-1	p. 353
18.3.2 Outer Loop Fuzzy Controller for LECS-1	p. 355
18.3.3 Results and Discussion for LECS-1	p. 359
18.4 Life-Extending Control of a Power Plant	p. 362
18.4.1 Inner Loop Feedback and Gain Scheduling	p. 364
18.4.2 Fuzzy Controller	p. 367
18.4.3 Results and Discussion	p. 372
18.5 Summary and Conclusions	p. 379
18.5.1 Control System Stability	p. 380
Acknowledgments	p. 381
Appendix A Brief Description of the Rocket Engine	p. 381
Appendix B Brief Description of the Power Plant	p. 382
References	p. 382
Epilogue	p. 385
Index	p. 387

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