Modern Adaptive Fuzzy Control Systems

161 Pages·2023·4.754 MB·English

by  Ardashir Mohammadzadeh, Mohammad Hosein Sabzalian, Chunwei Zhang, Oscar Castillo, Rathinasamy Sakthivel, Fayez F. M. El-Sousy

Studies in Fuzziness and Soft Computing
Ardashir Mohammadzadeh ·
Mohammad Hosein Sabzalian ·
Chunwei Zhang · Oscar Castillo ·
Rathinasamy Sakthivel ·
Fayez F. M. El-Sousy
Modern
Adaptive
Fuzzy Control
Systems
Studies in Fuzziness and Soft Computing
Volume 421
Series Editor
Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,
Warsaw, Poland
The series “Studies in Fuzziness and Soft Computing” contains publications on
various topics in the area of soft computing, which include fuzzy sets, rough sets,
neural networks, evolutionary computation, probabilistic and evidential reasoning,
multi-valued logic, and related fields. The publications within “Studies in Fuzziness
and Soft Computing” are primarily monographs and edited volumes. They cover
significant recent developments in the field, both of a foundational and applicable
character. An important feature of the series is its short publication time and
world-wide distribution. This permits a rapid and broad dissemination of research
results.
Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago.
All books published in the series are submitted for consideration in Web of Science.
·
Ardashir Mohammadzadeh
· ·
Mohammad Hosein Sabzalian Chunwei Zhang
· ·
Oscar Castillo Rathinasamy Sakthivel
Fayez F. M. El-Sousy
Modern Adaptive Fuzzy
Control Systems
Ardashir Mohammadzadeh Mohammad Hosein Sabzalian
Multidisciplinary Center for Infrastructure LabREI—Smart Grid Laboratory
Engineering (MCIE) Department of Systems and Energy
Shenyang University of Technology FEEC—School of Electrical and Computer
Shenyang, Liaoning, China Engineering
University of Campinas (UNICAMP)
Chunwei Zhang Campinas, Brazil
Multidisciplinary Center for Infrastructure
Engineering (MCIE) Oscar Castillo
Shenyang University of Technology Division of Graduate Studies
Shenyang, Liaoning, China Tijuana Institute of Technology
Tijuana, Baja California, Mexico
Rathinasamy Sakthivel
Department of Applied Mathematics Fayez F. M. El-Sousy
Bharathiar University Department of Electrical Engineering
Coimbatore, Tamil Nadu, India College of Engineering
Prince Sattam Bin Abdulaziz University
Al Kharj, Saudi Arabia
ISSN 1434-9922 ISSN 1860-0808 (electronic)
Studies in Fuzziness and Soft Computing
ISBN 978-3-031-17392-9 ISBN 978-3-031-17393-6 (eBook)
https://doi.org/10.1007/978-3-031-17393-6
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
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Preface
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 systems and different methods of training and opti-
mizing these systems. For this purpose, type-2 neuro-fuzzy systems are first analyzed
along with various methods of training and optimizing these systems through imple-
mentation in MATLAB. These systems are then employed to design adaptive fuzzy
controllers. The author tries to present all well-known optimization methods clearly
and code them in MATLAB. Furthermore, all materials are available at http://www.
simref.org, which can be visited by aficionados for faster in-depth learning. All dear
readers of this book are kindly asked to share their views about writing flaws and
scientific problems with us via the above website so that we can refine the book in the
next editions. In the end, we would like to thank Dr. Sahraneh Ghaemi, the esteemed
associate professor at University of Tabriz, and Dr. Ali Ahmadian, the esteemed
assistant professor of University of Bonab, who have helped us scientifically edit
this book.
Shenyang, China Ardashir Mohammadzadeh
Campinas, Brazil Mohammad Hosein Sabzalian
Shenyang, China Chunwei Zhang
Tijuana, Mexico Oscar Castillo
Coimbatore, India Rathinasamy Sakthivel
Al Kharj, Saudi Arabia Fayez F. M. El-Sousy
v
Contents
1 An Introduction to Fuzzy and Fuzzy Control Systems ............ 1
1.1 Historical Background .................................... 1
1.2 What is Adaptive Fuzzy Control? ........................... 2
1.3 Why Adaptive Fuzzy Control? ............................. 2
1.4 Problems in Adaptive Fuzzy Controller ...................... 3
References .................................................... 3
2 Classification of Adaptive Fuzzy Controllers ..................... 5
2.1 Direct Adaptive Fuzzy Controller ........................... 5
2.2 Indirect Adaptive Fuzzy Controller ......................... 5
2.3 Integrating Adaptive Fuzzy Controller with Other
Controllers .............................................. 6
2.3.1 Integrating Direct and Indirect Adaptive
Controllers ....................................... 6
2.3.2 Integrating Hybrid Fuzzy Controller with Other
Controllers to Compensate for Estimation Error ....... 6
2.3.3 Integrating Hybrid Fuzzy Controller with Output
Feedback Controller ............................... 6
2.3.4 Integrating Adaptive Fuzzy Controller with H∞
Control .......................................... 7
2.3.5 Integrating Adaptive Fuzzy Controller
with Supervised Controller ......................... 7
2.3.6 Integrating Adaptive Fuzzy Controller with Other
Control Methods .................................. 7
2.4 Different Classes of Nonlinear Systems ...................... 8
2.4.1 Affine Nonlinear Systems .......................... 8
2.4.2 Non-affine Nonlinear Systems ...................... 9
2.4.3 Nonlinear Feedback Systems ....................... 9
2.4.4 Nonlinear Pure-Feedback Systems .................. 10
2.4.5 Nonlinear Single-Input–Single-Output
and Multi-Input–Multi-Output Systems .............. 11
vii
viii Contents
2.4.6 Nonlinear Output and State Feedback Systems ........ 11
2.4.7 Discrete and Continuous Systems ................... 12
2.5 Adaptation Mechanism in Fuzzy Systems .................... 12
2.5.1 Setting Parameters ................................ 12
2.5.2 Setting Structure and Parameter ..................... 13
2.6 Conclusion .............................................. 13
References .................................................... 14
3 Type-2 Fuzzy Systems ......................................... 17
3.1 Introduction ............................................. 17
3.2 Singleton Fuzzy Systems .................................. 17
3.3 Non-singleton Fuzzy Systems .............................. 19
3.4 Features of Type-2 Fuzzy Systems .......................... 20
3.5 Basic Operations in Type-2 Fuzzy .......................... 21
3.6 Fuzzification ............................................ 22
3.7 Rules ................................................... 22
3.8 Logics .................................................. 23
3.9 Type Reduction .......................................... 24
3.10 Implementation in MATLAB .............................. 28
3.11 Designing a General Type-2 Fuzzy System with an Example ... 36
3.12 Interval Type-2 Fuzzy System .............................. 44
3.13 Conclusion .............................................. 46
References .................................................... 46
4 Training Interval Type-2 Fuzzy Systems Based on Error
Backpropagation .............................................. 49
4.1 Introduction ............................................. 49
4.2 Training Fuzzy Systems with Nie-Tan Type-Reduction ........ 49
4.2.1 Implementation in MATLAB ....................... 51
4.3 Fuzzy System with KM-EKM Type-Reduction ............... 51
4.4 Training Type-2 Fuzzy System with Extended Kalman Filter ... 52
4.5 Training Type-2 Fuzzy System Based on Genetic Algorithm .... 56
4.5.1 Introduction ...................................... 56
4.6 Calling Genetic Algorithm ................................. 59
4.7 Jargons of GA Toolkit in MATLAB ......................... 62
4.7.1 GA-Based Optimization of Neuro-Fuzzy System
Parameters ....................................... 68
4.8 Training Neural Networks Based on PSO .................... 71
4.8.1 Introduction ...................................... 71
4.9 Formulation of Algorithm ................................. 72
4.10 Implementation in MATLAB .............................. 74
4.11 Training Type-2 Fuzzy System Through Second-Order
Algorithms .............................................. 79
4.11.1 Introduction ...................................... 79
4.11.2 Newton’s Method ................................. 79
Contents ix
4.11.3 Levenberg–Marquardt Algorithm ................... 80
4.11.4 Conjugate Gradient Method ........................ 80
4.11.5 Implementation in MATLAB ....................... 81
4.12 Conclusion .............................................. 81
References .................................................... 93
5 Baseline Indirect Adaptive Control ............................. 95
5.1 Problem Specifications .................................... 95
5.2 Designing Fuzzy Controller ................................ 95
5.3 Designing Moderation Principle ............................ 97
5.4 Application in Moderation of Inverted Pendulum ............. 99
5.5 Conclusion .............................................. 101
References .................................................... 102
6 Type-2 Indirect Adaptive Control with Estimation Error
Approximation ................................................ 103
6.1 Introduction ............................................. 103
6.2 Literature Review ........................................ 103
6.3 Resistant Adaptive Fuzzy Control with Estimation Error
Elimination .............................................. 104
6.3.1 Problem Specifications ............................ 104
6.3.2 Estimating Uncertainties ........................... 104
6.3.3 Designing Controller .............................. 106
6.3.4 Designing Controller .............................. 110
6.3.5 Analysis of Stability and Inference of Adaptive
Rules ........................................... 112
6.3.6 Switching Mechanism ............................. 115
6.3.7 Applications ..................................... 116
6.4 Conclusion .............................................. 117
References .................................................... 117
7 Direct Adaptive Fuzzy Control ................................. 119
7.1 Introduction ............................................. 119
7.2 Literature Review ........................................ 119
7.2.1 Adaptive Fuzzy Control with Fewer Limitations ....... 120
7.2.2 Type-2 Fuzzy System ............................. 121
7.2.3 Simulation ....................................... 129
7.3 Conclusion .............................................. 130
References .................................................... 132
8 Direct Adaptive Fuzzy Control with a Self-regulated Structure .... 135
8.1 Introduction ............................................. 135
8.2 Literature Review ........................................ 135
8.3 Description of the Self-regulated Structure Algorithm ......... 136
8.4 Adaptation Rules in Self-regulated Adaptive Fuzzy
Controller ............................................... 140
8.5 Application in Inverted Pendulum Control ................... 142
x Contents
8.6 Conclusion .............................................. 143
References .................................................... 143
9 State Limitation Through Supervised Control ................... 145
9.1 Introduction ............................................. 145
9.2 Supervised Control for Indirect Adaptive Fuzzy Control
Systems ................................................. 145
9.3 Supervised Control for Fuzzy Control Systems in General ...... 147
9.4 Conclusion .............................................. 149
References .................................................... 149
10 Adaptive Sliding Fuzzy Control ................................ 151
10.1 Introduction ............................................. 151
10.2 Designing a Controller .................................... 151
10.3 Simulation .............................................. 154
10.4 Conclusion .............................................. 157