Modern Adaptive Fuzzy Control Systems

translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Preface Contents 1 An Introduction to Fuzzy and Fuzzy Control Systems 1.1 Historical Background 1.2 What is Adaptive Fuzzy Control? 1.3 Why Adaptive Fuzzy Control? 1.4 Problems in Adaptive Fuzzy Controller References 2 Classification of Adaptive Fuzzy Controllers 2.1 Direct Adaptive Fuzzy Controller 2.2 Indirect Adaptive Fuzzy Controller 2.3 Integrating Adaptive Fuzzy Controller with Other Controllers 2.3.1 Integrating Direct and Indirect Adaptive Controllers 2.3.2 Integrating Hybrid Fuzzy Controller with Other Controllers to Compensate for Estimation Error 2.3.3 Integrating Hybrid Fuzzy Controller with Output Feedback Controller 2.3.4 Integrating Adaptive Fuzzy Controller with Hinfty Control 2.3.5 Integrating Adaptive Fuzzy Controller with Supervised Controller 2.3.6 Integrating Adaptive Fuzzy Controller with Other Control Methods 2.4 Different Classes of Nonlinear Systems 2.4.1 Affine Nonlinear Systems 2.4.2 Non-affine Nonlinear Systems 2.4.3 Nonlinear Feedback Systems 2.4.4 Nonlinear Pure-Feedback Systems 2.4.5 Nonlinear Single-Input–Single-Output and Multi-Input–Multi-Output Systems 2.4.6 Nonlinear Output and State Feedback Systems 2.4.7 Discrete and Continuous Systems 2.5 Adaptation Mechanism in Fuzzy Systems 2.5.1 Setting Parameters 2.5.2 Setting Structure and Parameter 2.6 Conclusion References 3 Type-2 Fuzzy Systems 3.1 Introduction 3.2 Singleton Fuzzy Systems 3.3 Non-singleton Fuzzy Systems 3.4 Features of Type-2 Fuzzy Systems 3.5 Basic Operations in Type-2 Fuzzy 3.6 Fuzzification 3.7 Rules 3.8 Logics 3.9 Type Reduction 3.10 Implementation in MATLAB 3.11 Designing a General Type-2 Fuzzy System with an Example 3.12 Interval Type-2 Fuzzy System 3.13 Conclusion References 4 Training Interval Type-2 Fuzzy Systems Based on Error Backpropagation 4.1 Introduction 4.2 Training Fuzzy Systems with Nie-Tan Type-Reduction 4.2.1 Implementation in MATLAB 4.3 Fuzzy System with KM-EKM Type-Reduction 4.4 Training Type-2 Fuzzy System with Extended Kalman Filter 4.5 Training Type-2 Fuzzy System Based on Genetic Algorithm 4.5.1 Introduction 4.6 Calling Genetic Algorithm 4.7 Jargons of GA Toolkit in MATLAB 4.7.1 GA-Based Optimization of Neuro-Fuzzy System Parameters 4.8 Training Neural Networks Based on PSO 4.8.1 Introduction 4.9 Formulation of Algorithm 4.10 Implementation in MATLAB 4.11 Training Type-2 Fuzzy System Through Second-Order Algorithms 4.11.1 Introduction 4.11.2 Newton’s Method 4.11.3 Levenberg–Marquardt Algorithm 4.11.4 Conjugate Gradient Method 4.11.5 Implementation in MATLAB 4.12 Conclusion References 5 Baseline Indirect Adaptive Control 5.1 Problem Specifications 5.2 Designing Fuzzy Controller 5.3 Designing Moderation Principle 5.4 Application in Moderation of Inverted Pendulum 5.5 Conclusion References 6 Type-2 Indirect Adaptive Control with Estimation Error Approximation 6.1 Introduction 6.2 Literature Review 6.3 Resistant Adaptive Fuzzy Control with Estimation Error Elimination 6.3.1 Problem Specifications 6.3.2 Estimating Uncertainties 6.3.3 Designing Controller 6.3.4 Designing Controller 6.3.5 Analysis of Stability and Inference of Adaptive Rules 6.3.6 Switching Mechanism 6.3.7 Applications 6.4 Conclusion References 7 Direct Adaptive Fuzzy Control 7.1 Introduction 7.2 Literature Review 7.2.1 Adaptive Fuzzy Control with Fewer Limitations 7.2.2 Type-2 Fuzzy System 7.2.3 Simulation 7.3 Conclusion References 8 Direct Adaptive Fuzzy Control with a Self-regulated Structure 8.1 Introduction 8.2 Literature Review 8.3 Description of the Self-regulated Structure Algorithm 8.4 Adaptation Rules in Self-regulated Adaptive Fuzzy Controller 8.5 Application in Inverted Pendulum Control 8.6 Conclusion References 9 State Limitation Through Supervised Control 9.1 Introduction 9.2 Supervised Control for Indirect Adaptive Fuzzy Control Systems 9.3 Supervised Control for Fuzzy Control Systems in General 9.4 Conclusion References 10 Adaptive Sliding Fuzzy Control 10.1 Introduction 10.2 Designing a Controller 10.3 Simulation 10.4 Conclusion 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.