Introduction To Type-2 Fuzzy Logic Control

An introductory book that provides theoretical, practical,
and application coverage of the emerging field of type-2 fuzzy
logic control

Until recently, little was known about type-2 fuzzy controllers
due to the lack of basic calculation methods available for type-2
fuzzy sets and logic--and many different aspects of type-2
fuzzy control still needed to be investigated in order to advance
this new and powerful technology. This self-contained reference
covers everything readers need to know about the growing field.

Written with an educational focus in mind, Introduction to
Type-2 Fuzzy Logic Control: Theory and Applications uses a
coherent structure and uniform mathematical notations to link
chapters that are closely related, reflecting the book's
central themes: analysis and design of type-2 fuzzy control
systems. The book includes worked examples, experiment and
simulation results, and comprehensive reference materials. The book
also offers downloadable computer programs from an associated
website.

Presented by world-class leaders in type-2 fuzzy logic control,
Introduction to Type-2 Fuzzy Logic Control:

• Is useful for any technical person interested in learning
  type-2 fuzzy control theory and its applications

• Offers experiment and simulation results via downloadable
  computer programs

• Features type-2 fuzzy logic background chapters to make the
  book self-contained

• Provides an extensive literature survey on both fuzzy logic and
  related type-2 fuzzy control

Introduction to Type-2 Fuzzy Logic Control is an
easy-to-read reference book suitable for engineers, researchers,
and graduate students who want to gain deep insight into type-2
fuzzy logic control.

Autorentext

JERRY M. MENDEL is Professor in the Ming Hsieh Department
of Electrical Engineering at the University of Southern California,
Life Fellow of the IEEE, and a Distinguished Member of the IEEE
Control Systems Society.

HANI HAGRAS is Professor and Director of the
Computational Intelligence Centre in the School of Computer Science
and Electronic Engineering at the University of Essex, UK, and is a
Fellow of the IEEE.

WOEI-WAN TAN is Associate Professor in the Department of
Electrical Engineering at the National University of Singapore.

WILLIAM W. MELEK is Associate Professor in the Department
of Mechanical and Mechatronics Engineering at the University of
Waterloo.

HAO YING is Professor in the Department of Electrical and
Computer Engineering at Wayne State University and a Fellow of the
IEEE.

Zusammenfassung

An introductory book that provides theoretical, practical, and application coverage of the emerging field of type-2 fuzzy logic control

Until recently, little was known about type-2 fuzzy controllers due to the lack of basic calculation methods available for type-2 fuzzy sets and logicand many different aspects of type-2 fuzzy control still needed to be investigated in order to advance this new and powerful technology. This self-contained reference covers everything readers need to know about the growing field.

Written with an educational focus in mind, Introduction to Type-2 Fuzzy Logic Control: Theory and Applications uses a coherent structure and uniform mathematical notations to link chapters that are closely related, reflecting the book's central themes: analysis and design of type-2 fuzzy control systems. The book includes worked examples, experiment and simulation results, and comprehensive reference materials. The book also offers downloadable computer programs from an associated website.

Presented by world-class leaders in type-2 fuzzy logic control, Introduction to Type-2 Fuzzy Logic Control:

• Is useful for any technical person interested in learning type-2 fuzzy control theory and its applications
• Offers experiment and simulation results via downloadable computer programs
• Features type-2 fuzzy logic background chapters to make the book self-contained
• Provides an extensive literature survey on both fuzzy logic and related type-2 fuzzy control
  Introduction to Type-2 Fuzzy Logic Control is an easy-to-read reference book suitable for engineers, researchers, and graduate students who want to gain deep insight into type-2 fuzzy logic control.

Inhalt
Preface xiii Contributors xvii

1 Introduction 1

1.1 Early History of Fuzzy Control 1

1.2 What Is a Type-1 Fuzzy Set? 2

1.3 What Is a Type-1 Fuzzy Logic Controller? 3

1.4 What Is a Type-2 Fuzzy Set? 7

1.5 What Is a Type-2 Fuzzy Logic Controller? 9

1.6 Distinguishing an FLC from Other Nonlinear Controllers 10

1.7 T2 FLCs versus T1 FLCs 11

1.8 Real-World Applications of IT2 Mamdani FLCs 14

1.8.1 Applications to Industrial Control 14

1.8.2 Airplane Altitude Control 23

1.8.3 Control of Mobile Robots 24

1.8.4 Control of Ambient Intelligent Environments 27

1.9 Book Rationale 29

1.10 Software and How it Can Be Accessed 30

1.11 Coverage of the Other Chapters 30

2 Introduction to Type-2 Fuzzy Sets 32

2.1 Introduction 32

2.2 Brief Review of Type-1 Fuzzy Sets 32

2.2.1 Some Definitions 32

2.2.2 Set-Theoretic Operations 35

2.2.3 Alpha Cuts 36

2.2.4 Compositions of T1 FSs 39

2.2.5 Rules and Their MFs 40

2.3 Interval Type-2 Fuzzy Sets 42

2.3.1 Introduction 42

2.3.2 Definitions 43

2.3.3 Set-Theoretic Operations 51

2.3.4 Centroid of an IT2 FS 54

2.3.5 Properties of cl(k) and cr(k) 58

2.3.6 KM Algorithms as Well as Some Others 59

2.4 General Type-2 Fuzzy Sets 68

2.4.1 -Plane/zSlice Representation 68

2.4.2 Set-Theoretic Operations 72

2.4.3 Centroid of a GT2 FS 73

2.5 Wrapup 77

2.6 Moving On 79

3 Interval Type-2 Fuzzy Logic Controllers 80

3.1 Introduction 80

3.2 Type-1 Fuzzy Logic Controllers 80

3.2.1 Introduction 80

3.2.2 T1 Mamdani FLCs 81

3.2.3 T1 TSK FLCs 85

3.2.4 Design of T1 FLCs 86

3.3 Interval Type-2 Fuzzy Logic Controllers 86

3.3.1 Introduction 86

3.3.2 IT2 Mamdani FLCs 87

3.3.3 IT2 TSK FLCs 103

3.3.4 Design of T2 FLCs 105

3.4 WuMendel Uncertainty Bounds 105

3.5 Control Analyses of IT2 FLCs 111

3.6 Determining the FOU Parameters of IT2 FLCs 114

3.6.1 Blurring T1 MFs 114

3.6.2 Optimizing FOU Parameters 114

3.7 Moving On 122

Appendix 3A. Proof of Theorem 3.4 123

3A.1 Inner-Bound Set [ul(), ur()] 123

3A.2 Outer-Bound Set [ul(), ur()] 124

4 Analytical Structure of Various Interval Type-2 Fuzzy PI and PD Controllers 131

4.1 Introduction 131

4.2 PID, PI, and PD Controllers and Their Relationships 134

4.2.1 Two Forms of PID ControllerPosition Form and Incremental Form 134

4.2.2 PI and PD Controllers and Their Relationship 135

4.3 Components of the Interval T2 Fuzzy PI and PD Controllers 136

4.4 Mamdani Fuzzy PI and PD ControllersConfiguration 1 140

4.4.1 Fuzzy PI Controller Configuration 140

4.4.2 Method for Deriving the Analytical Structure 144

4.5 Mamdani Fuzzy PI and PD ControllersConfiguration 2 154

4.6 Mamdani Fuzzy PI and PD ControllersConfiguration 3 162

4.6.1 Fuzzy PI Controller Configuration 162

4.6.2 Method for Deriving the Analytical Structure 165

4.7 Mamdani Fuzzy PI and PD ControllersConfiguration 4 169

4.7.1 Fuzzy PI Controller Configuration 169

4.7.2 Method for Deriving the Analytical Structure 171

4.8 TSK Fuzzy PI and PD ControllersConfiguration 5 181

4.8.1 Fuzzy PI Controller Configuration 181

4.8.2 Deriving the Analytical Structure 184

4.9 Analyzing the Derived Analytical Structures 185

4.9.1 Structural Connection with the Corresponding T1 Fuzzy PI Controller 186

4.9.2 Characteristics of the Variable Gains of the T2 Fuzzy PI Controller 190

4.10 Design Guidelines for the T2 Fuzzy PI and PD Controllers 194

4.10.1 Determination of 1 and 2 Values 196

4.1…