Robust Control Optimization with Metaheuristics

Philippe Feyel is an R&D Engineer for the high-tech company Sagem Défense Sécurité, part of the defence and security business of the SAFRAN group, in Paris, France.

• Preface  ixIntroduction and Motivations  xiChapter 1. Metaheuristics for Controller Optimization  11.1. Introduction  11.2. Evolutionary approaches using differential evolution  21.2.1. Standard version 21.2.2. Perturbed version 71.3. Swarm approaches 81.3.1. Particle swarm optimization algorithm 81.3.2. Quantum particle swarm algorithm 141.3.3. Artificial bee colony optimization algorithm  201.3.4. Cuckoo search algorithm 251.3.5. Firefly algorithm 311.4. Summary  33Chapter 2. Reformulation of Robust Control Problems for Stochastic Optimization  352.1. Introduction  352.2. H∞ synthesis  352.2.1. Full H∞ synthesis 352.2.2. Fixed-structure H∞ synthesis 452.2.3. Formulating H∞ synthesis for stochastic optimization 672.2.4. Conclusion 1052.3. μ-Synthesis 1052.3.1. The problem of performance robustness  1052.3.2. μ-Synthesis  1102.4. LPV/LFT synthesis  1402.4.1. Introduction  1402.4.2. The LPV/LFT controller synthesis problem  1412.4.3. Reformulation for stochastic optimization 147Chapter 3. Optimal Tuning of Structured and Robust H∞ Controllers Against High-level Requirements 1713.1. Introduction and motivations 1713.2. Loop-shaping H∞ synthesis  1803.2.1. Approach principle  1803.2.2. Generalized gain and phase margins  1843.2.3. Four-block interpretation of the method  1853.2.4. Practical implementation 1863.2.5. Implementation of controllers  1903.3. A generic method for the declination of requirements 1943.3.1. General principles 1943.3.2. Special cases 1963.3.3. Management of requirement priority level 1973.4. Optimal tuning of weighting functions 1983.4.1. Optimization on nominal plant 1983.4.2. Multiple plant optimization 2023.4.3. Applicative example – inertial stabilization of line of sight  2073.5. Optimal tuning of the fixed-structure and fixed-order final controller 2383.5.1. Introduction  2383.5.2. Toward eliminating weighting functions  2403.5.3. Extensions to the approach  2593.5.4. Link with standard control problems  277Chapter 4. HinfStoch: A Toolbox for Structured and Robust Controller Computation Based on Stochastic Optimization 2794.1. Introduction  2794.2. Structured multiple plant H∞ synthesis 2804.2.1. Principle  2804.2.2. Formalism 2804.3. Structured μ-synthesis 2844.3.1. Principle  2844.3.2. Formalism 2854.4. Structured LPV/LFT synthesis  2884.4.1. Principle  2884.4.2. Formalism 2894.5. Structured and robust synthesis against high-level requirements with HinfStoch_ControllerTuning 2924.5.1. Principle  2924.5.2. Formalism 2934.5.3. Examples 311Appendices 351Appendix A. Notions of Coprime Factorizations  353Appendix B. Examples of LFT Form Used for Uncertain Systems  359Appendix C. LFT Form Use of an Electromechanical System with Uncertain Flexible Modes  365Appendix D. FTM (1D) Computation from a Time Signal 383Appendix E. Choice of Iteration Number for CompLeib Tests  385Appendix F. PDE versus DE 393Bibliography 399Index 407