Fuzzy Neural Networks for Real Time Control Applications

Concepts, Modeling and Algorithms for Fast Learning

Erdal Kayacan, Mojtaba Ahmadieh Khanesar

• Publisher: Butterworth-Heinemann
• Year: 2015
• Print ISBN: 9780128026878
• eBook ISBN: 9780128027035
• Topic: Mathematics
• Subtopic: Artificial Intelligence (AI) & Semantics
• Index: Mathematics

AN INDISPENSABLE RESOURCE FOR ALL THOSE WHO DESIGN AND IMPLEMENT TYPE-1 AND TYPE-2 FUZZY NEURAL NETWORKS IN REAL TIME SYSTEMS Delve into the type-2 fuzzy logic systems and become engrossed in the parameter update algorithms for type-1 and type-2 fuzzy neural networks and their stability analysis with this book! Not only does this book stand apart from others in its focus but also in its application-based presentation style. Prepared in a way that can be easily understood by those who are experienced and inexperienced in this field. Readers can benefit from the computer source codes for both identification and control purposes which are given at the end of the book. A clear and an in-depth examination has been made of all the necessary mathematical foundations, type-1 and type-2 fuzzy neural network structures and their learning algorithms as well as their stability analysis. You will find that each chapter is devoted to a different learning algorithm for the tuning of type-1 and type-2 fuzzy neural networks; some of which are: • Gradient descent • Levenberg-Marquardt • Extended Kalman filter In addition to the aforementioned conventional learning methods above, number of novel sliding mode control theory-based learning algorithms, which are simpler and have closed forms, and their stability analysis have been proposed. Furthermore, hybrid methods consisting of particle swarm optimization and sliding mode control theory-based algorithms have also been introduced. The potential readers of this book are expected to be the undergraduate and graduate students, engineers, mathematicians and computer scientists. Not only can this book be used as a reference source for a scientist who is interested in fuzzy neural networks and their real-time implementations but also as a course book of fuzzy neural networks or artificial intelligence in master or doctorate university studies. We hope that this book will serve its main purpose successfully. - Parameter update algorithms for type-1 and type-2 fuzzy neural networks and their stability analysis - Contains algorithms that are applicable to real time systems - Introduces fast and simple adaptation rules for type-1 and type-2 fuzzy neural networks - Number of case studies both in identification and control - Provides MATLAB® codes for some algorithms in the book

Chapter 1

Mathematical Preliminaries

Abstract

This chapter summarizes the basic mathematical preliminaries for a better understanding of the consecutive chapters. The given materials include the notations, definitions and related equations.

Keywords

Matrix

Matrix inversion

Functions

Taylor expansion

Gradient

Hessian matrix

Stability analysis

Lyapunov function

Contents

1.1 Introduction 1

1.2 Linear Matrix Algebra 1

1.3 Function 4

1.4 Stability Analysis 5

1.5 Sliding Mode Control Theory 7

1.6 Conclusion 11

References 11

1.1 Introduction

Design, optimization and parameter tuning of FNNs require fundamental knowledge about matrix theory, linear algebra, function approximation, partial derivatives, nonlinear programming, state estimation and nonlinear stability analysis. Although this chapter summarizes a few fundamental mathematical preliminaries that will allow the reader to follow the consecutive chapters easier, they are selective, and serve only as a reference for the notations and theories used in this book. F...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Foreword
• Preface
• Acknowledgments
• List of Acronyms/Abbreviations
• Chapter 1: Mathematical Preliminaries
• Chapter 2: Fundamentals of Type-1 Fuzzy Logic Theory
• Chapter 3: Fundamentals of Type-2 Fuzzy Logic Theory
• Chapter 4: Type-2 Fuzzy Neural Networks
• Chapter 5: Gradient Descent Methods for Type-2 Fuzzy Neural Networks
• Chapter 6: Extended Kalman Filter Algorithm for the Tuning of Type-2 Fuzzy Neural Networks
• Chapter 7: Sliding Mode Control Theory-Based Parameter Adaptation Rules for Fuzzy Neural Networks
• Chapter 8: Hybrid Training Method for Type-2 Fuzzy Neural Networks Using Particle Swarm Optimization
• Chapter 9: Noise Reduction Property of Type-2 Fuzzy Neural Networks
• Chapter 10: Case Studies: Identification Examples
• Chapter 11: Case Studies: Control Examples
• Appendix A
• Appendix B
• Index