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.
Author(s): Ardashir Mohammadzadeh, Mohammad Hosein Sabzalian, Chunwei Zhang, Oscar Castillo, Rathinasamy Sakthivel, Fayez F. M. El-Sousy
Series: Studies in Fuzziness and Soft Computing, 421
Publisher: Springer
Year: 2022
Language: English
Pages: 160
City: Cham
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
