Robust Control Optimization with Metaheuristics

Preface ix
Introduction and Motivations xi
Chapter 1. Metaheuristics for Controller Optimization 1
1.1. Introduction 1
1.2. Evolutionary approaches using differential evolution 2
1.2.1. Standard version 2
1.2.2. Perturbed version 7
1.3. Swarm approaches 8
1.3.1. Particle swarm optimization algorithm 8
1.3.2. Quantum particle swarm algorithm 14
1.3.3. Artificial bee colony optimization algorithm 20
1.3.4. Cuckoo search algorithm 25
1.3.5. Firefly algorithm 31
1.4. Summary 33
Chapter 2. Reformulation of Robust Control Problems for Stochastic Optimization 35
2.1. Introduction 35
2.2. H infinity synthesis 35
2.2.1. Full H infinity synthesis 35
2.2.2. Fixed-structure H infinity synthesis 45
2.2.3. Formulating H infinity synthesis for stochastic optimization 67
2.2.4. Conclusion 105
2.3. mu-Synthesis 105
2.3.1. The problem of performance robustness 105
2.3.2. mu-Synthesis 110
2.4. LPV/LFT synthesis 140
2.4.1. Introduction 140
2.4.2. The LPV/LFT controller synthesis problem 141
2.4.3. Reformulation for stochastic optimization 147
Chapter 3. Optimal Tuning of Structured and Robust H infinity Controllers Against High-level Requirements 171
3.1. Introduction and motivations 171
3.2. Loop-shaping H infinity synthesis 180
3.2.1. Approach principle 180
3.2.2. Generalized gain and phase margins 184
3.2.3. Four-block interpretation of the method 185
3.2.4. Practical implementation 186
3.2.5. Implementation of controllers 190
3.3. A generic method for the declination of requirements 194
3.3.1. General principles 194
3.3.2. Special cases 196
3.3.3. Management of requirement priority level 197
3.4. Optimal tuning of weighting functions 198
3.4.1. Optimization on nominal plant 198
3.4.2. Multiple plant optimization 202
3.4.3. Applicative example - inertial stabilization of line of sight 207
3.5. Optimal tuning of the fixed-structure and fixed-order final controller 238
3.5.1. Introduction 238
3.5.2. Toward eliminating weighting functions 240
3.5.3. Extensions to the approach 259
3.5.4. Link with standard control problems 277
Chapter 4. HinfStoch: A Toolbox for Structured and Robust Controller Computation Based on Stochastic Optimization 279
4.1. Introduction 279
4.2. Structured multiple plant H infinity synthesis 280
4.2.1. Principle 280
4.2.2. Formalism 280
4.3. Structured mu-synthesis 284
4.3.1. Principle 284
4.3.2. Formalism 285
4.4. Structured LPV/LFT synthesis 288
4.4.1. Principle 288
4.4.2. Formalism 289
4.5. Structured and robust synthesis against high-level requirements with HinfStoch_ControllerTuning 292
4.5.1. Principle 292
4.5.2. Formalism 293
4.5.3. Examples 311
Appendices 351
Appendix A. Notions of Coprime Factorizations 353
Appendix B. Examples of LFT Form Used for Uncertain Systems 359
Appendix C. LFT Form Use of an Electromechanical System with Uncertain Flexible Modes 365
Appendix D. FTM (1D) Computation from a Time Signal 383
Appendix E. Choice of Iteration Number for CompLeib Tests 385
Appendix F. PDE versus DE 393
Bibliography 399
Index 407