Modern Adaptive Fuzzy Control Systems

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Preface 6 Contents 7 1 An Introduction to Fuzzy and Fuzzy Control Systems 11 1.1 Historical Background 11 1.2 What is Adaptive Fuzzy Control? 12 1.3 Why Adaptive Fuzzy Control? 12 1.4 Problems in Adaptive Fuzzy Controller 13 References 13 2 Classification of Adaptive Fuzzy Controllers 14 2.1 Direct Adaptive Fuzzy Controller 14 2.2 Indirect Adaptive Fuzzy Controller 14 2.3 Integrating Adaptive Fuzzy Controller with Other Controllers 15 2.3.1 Integrating Direct and Indirect Adaptive Controllers 15 2.3.2 Integrating Hybrid Fuzzy Controller with Other Controllers to Compensate for Estimation Error 15 2.3.3 Integrating Hybrid Fuzzy Controller with Output Feedback Controller 15 2.3.4 Integrating Adaptive Fuzzy Controller with Hinfty Control 16 2.3.5 Integrating Adaptive Fuzzy Controller with Supervised Controller 16 2.3.6 Integrating Adaptive Fuzzy Controller with Other Control Methods 16 2.4 Different Classes of Nonlinear Systems 17 2.4.1 Affine Nonlinear Systems 17 2.4.2 Non-affine Nonlinear Systems 18 2.4.3 Nonlinear Feedback Systems 18 2.4.4 Nonlinear Pure-Feedback Systems 19 2.4.5 Nonlinear Single-Input–Single-Output and Multi-Input–Multi-Output Systems 20 2.4.6 Nonlinear Output and State Feedback Systems 20 2.4.7 Discrete and Continuous Systems 21 2.5 Adaptation Mechanism in Fuzzy Systems 21 2.5.1 Setting Parameters 21 2.5.2 Setting Structure and Parameter 22 2.6 Conclusion 22 References 23 3 Type-2 Fuzzy Systems 26 3.1 Introduction 26 3.2 Singleton Fuzzy Systems 26 3.3 Non-singleton Fuzzy Systems 28 3.4 Features of Type-2 Fuzzy Systems 29 3.5 Basic Operations in Type-2 Fuzzy 30 3.6 Fuzzification 31 3.7 Rules 31 3.8 Logics 32 3.9 Type Reduction 33 3.10 Implementation in MATLAB 37 3.11 Designing a General Type-2 Fuzzy System with an Example 45 3.12 Interval Type-2 Fuzzy System 53 3.13 Conclusion 55 References 55 4 Training Interval Type-2 Fuzzy Systems Based on Error Backpropagation 57 4.1 Introduction 57 4.2 Training Fuzzy Systems with Nie-Tan Type-Reduction 57 4.2.1 Implementation in MATLAB 59 4.3 Fuzzy System with KM-EKM Type-Reduction 59 4.4 Training Type-2 Fuzzy System with Extended Kalman Filter 60 4.5 Training Type-2 Fuzzy System Based on Genetic Algorithm 64 4.5.1 Introduction 64 4.6 Calling Genetic Algorithm 67 4.7 Jargons of GA Toolkit in MATLAB 70 4.7.1 GA-Based Optimization of Neuro-Fuzzy System Parameters 76 4.8 Training Neural Networks Based on PSO 79 4.8.1 Introduction 79 4.9 Formulation of Algorithm 80 4.10 Implementation in MATLAB 82 4.11 Training Type-2 Fuzzy System Through Second-Order Algorithms 87 4.11.1 Introduction 87 4.11.2 Newton’s Method 87 4.11.3 Levenberg–Marquardt Algorithm 88 4.11.4 Conjugate Gradient Method 88 4.11.5 Implementation in MATLAB 89 4.12 Conclusion 89 References 101 5 Baseline Indirect Adaptive Control 102 5.1 Problem Specifications 102 5.2 Designing Fuzzy Controller 102 5.3 Designing Moderation Principle 104 5.4 Application in Moderation of Inverted Pendulum 106 5.5 Conclusion 108 References 109 6 Type-2 Indirect Adaptive Control with Estimation Error Approximation 110 6.1 Introduction 110 6.2 Literature Review 110 6.3 Resistant Adaptive Fuzzy Control with Estimation Error Elimination 111 6.3.1 Problem Specifications 111 6.3.2 Estimating Uncertainties 111 6.3.3 Designing Controller 113 6.3.4 Designing Controller 117 6.3.5 Analysis of Stability and Inference of Adaptive Rules 119 6.3.6 Switching Mechanism 122 6.3.7 Applications 123 6.4 Conclusion 124 References 124 7 Direct Adaptive Fuzzy Control 125 7.1 Introduction 125 7.2 Literature Review 125 7.2.1 Adaptive Fuzzy Control with Fewer Limitations 126 7.2.2 Type-2 Fuzzy System 127 7.2.3 Simulation 135 7.3 Conclusion 136 References 138 8 Direct Adaptive Fuzzy Control with a Self-regulated Structure 140 8.1 Introduction 140 8.2 Literature Review 140 8.3 Description of the Self-regulated Structure Algorithm 141 8.4 Adaptation Rules in Self-regulated Adaptive Fuzzy Controller 145 8.5 Application in Inverted Pendulum Control 147 8.6 Conclusion 148 References 148 9 State Limitation Through Supervised Control 150 9.1 Introduction 150 9.2 Supervised Control for Indirect Adaptive Fuzzy Control Systems 150 9.3 Supervised Control for Fuzzy Control Systems in General 152 9.4 Conclusion 154 References 154 10 Adaptive Sliding Fuzzy Control 155 10.1 Introduction 155 10.2 Designing a Controller 155 10.3 Simulation 158 10.4 Conclusion 161 This book explains the basic concepts, theory and applications of fuzzy systems in control in a simple unified approach with clear ex-amples and simulations in the MATLAB programming language. Fuzzy systems, especially, type-2 neuro-fuzzy systems, are now used extensively in various engineering fields for different purposes. In plain language, this book aims to practically explain fuzzy sys-tems and different methods of training and optimizing these systems. For this purpose, type-2 neuro-fuzzy systems are first analyzed along with various methods of training and optimizing these systems through implementation in MATLAB. These systems are then em-ployed to design adaptive fuzzy controllers. The authors aim at pre-senting all the well-known optimization methods clearly and code them in the MATLAB language.