Chemical Optimization Algorithm for Fuzzy Controller Design (SpringerBriefs in Applied Sciences and Technology)

In this book, a novel optimization method inspired by a paradigm from nature is introduced. The chemical reactions are used as a paradigm to propose an optimization method that simulates these natural processes. The proposed algorithm is described in detail and then a set of typical complex benchmark functions is used to evaluate the performance of the algorithm. Simulation results show that the proposed optimization algorithm can outperform other methods in a set of benchmark functions. This chemical reaction optimization paradigm is also applied to solve the tracking problem for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on fuzzy logic theory. Computer simulations are presented confirming that this optimization paradigm is able to outperform other optimization techniques applied to this particular robot application. Preface 5 Contents 7 1 Introduction 9 Abstract 9 References 10 2 Theory and Background 12 Abstract 12 2.1 Nature-Inspired Metaheuristics 12 2.2 Artificial Chemistry 13 2.2.1 The Set of Molecules S 13 2.2.2 The Set of Rules R 14 2.2.3 Reactor Algorithm A–Dynamics 14 2.3 Fuzzy Logic 14 2.3.1 Fuzzy Sets 14 2.3.2 Fuzzy Logic Controller 15 2.4 Related Work 15 References 16 3 Chemical Definitions 17 Abstract 17 3.1 Chemical Definitions 17 Reference 18 4 The Proposed Chemical Reaction Algorithm 19 Abstract 19 4.1 ElementsCompounds 21 4.2 Chemical Reactions 21 4.3 Synthesis Reactions 22 4.4 Decomposition Reactions 22 4.5 Single-Substitution Reactions 23 4.6 Double-Substitution Reactions 23 References 24 5 Application Problems 25 Abstract 25 5.1 Complex Benchmark Functions 25 5.2 Control of an Autonomous Mobile Robot Using Fuzzy Logic 26 5.2.1 Definition of the Mobile Robot 27 5.2.2 Tracking Controller of Mobile Robot 28 5.2.3 Control of the Kinematic model 28 5.2.4 The Fuzzy Logic Tracking Controller 30 5.3 Control of an Autonomous Mobile Robot Using Type-2 Fuzzy Logic 30 References 31 6 Simulation Results 33 Abstract 33 6.1 Results of the CRA Applied to the Complex Benchmark Functions 33 6.2 Results of the CRA Applied to the Fuzzy Control of an Autonomous Mobile Robot 36 6.2.1 Finding k1, k2, k3 36 6.2.2 Optimization of a Fuzzy Logic Controller 43 6.2.2.1 Case 1 46 6.2.2.2 Case 2 47 6.2.2.3 Case 3 48 6.2.3 Best Result Applying GAs 50 6.3 Optimization of a Type-2 Fuzzy Logic Controller 52 References 62 7 Conclusions 63 Abstract 63 Reference 64 Appendix A 65 Appendix B 72 Index 81 Front Matter....Pages i-viii Introduction....Pages 1-3 Theory and Background....Pages 5-9 Chemical Definitions....Pages 11-12 The Proposed Chemical Reaction Algorithm....Pages 13-18 Application Problems....Pages 19-26 Simulation Results....Pages 27-56 Conclusions....Pages 57-58 Back Matter....Pages 59-77