Lin Xiao, Lei Jia

Zeroing Neural Networks

Finite-Time Convergence Design, Analysis and Applications

• Gebundenes Buch

Produktbeschreibung

Zeroing Neural Networks

Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems

Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps.

Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book:
_ Describes how to design, analyze, and apply FTZNN models for solving computational problems
_ Presents multiple FTZNN models for solving time-varying computational problems
_ Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments
_ Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter

Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.

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Produktdetails

• Verlag: Wiley & Sons / Wiley-IEEE Press
• Artikelnr. des Verlages: 1W119985990
• 1. Auflage
• Seitenzahl: 432
• Erscheinungstermin: 1. Dezember 2022
• Englisch
• Abmessung: 235mm x 157mm x 27mm
• Gewicht: 666g
• ISBN-13: 9781119985990
• ISBN-10: 1119985994
• Artikelnr.: 63987653

Autorenporträt

LIN XIAO, PhD, is a Professor in the College of Information Science and Engineering at Hunan Normal University, Changsha, China. He has authored more than 100 papers in international conferences and journals, including IEEE-TCYB, IEEE-TII, IEEE-TSMCS. Professor Xiao is Associate Editor of IEEE-TNNLS. LEI JIA is a PhD degree candidate in Operations Research and Control in the College of Mathematics and Statistics at Hunan Normal University, Changsha, China. She has authored or co-authored more than 20 scientific articles, including 13 IEEE-transaction papers.

Inhaltsangabe

List of Figures xv

List of Tables xxxi

Author Biographies xxxiii

Preface xxxv

Acknowledgments xlv

Part I Application to Matrix Square Root 1

1 FTZNN for Time-varying Matrix Square Root 3

1.1 Introduction 3

1.2 Problem Formulation and ZNN Model 4

1.3 FTZNN Model 4

1.3.1 Model Design 5

1.3.2 Theoretical Analysis 7

1.4 Illustrative Verification 8

1.5 Chapter Summary 11

References 11

2 FTZNN for Static Matrix Square Root 13

2.1 Introduction 13

2.2 Solution Models 14

2.2.1 OZNN Model 14

2.2.2 FTZNN Model 15

2.3 Illustrative Verification 17

2.3.1 Example 1 18

2.3.2 Example 2 20

2.4 Chapter Summary 21

References 21

Part II Application to Matrix Inversion 23

3 Design Scheme I of FTZNN 25

3.1 Introduction 25

3.2 Problem Formulation and Preliminaries 25

3.3 FTZNN Model 26

3.3.1 Model Design 26

3.3.2 Theoretical Analysis 29

3.4 Illustrative Verification 30

3.4.1 Example 1: Nonrandom Time-varying Coefficients 30

3.4.2 Example 2: Random Time-varying Coefficients 34

3.5 Chapter Summary 35

References 36

4 Design Scheme II of FT ZNN 39

4.1 Introduction 39

4.2 Preliminaries 40

4.2.1 Mathematical Preparation 40

4.2.2 Problem Formulation 41

4.3 NT-FTZNN Model 41

4.4 Theoretical Analysis 43

4.4.1 NT-FTZNN in the Absence of Noises 43

4.4.2 NT-FTZNN in the Presence of Noises 44

4.5 Illustrative Verification 46

4.5.1 Example 1: Two-dimensional Coefficient 47

4.5.2 Example 2: Six-dimensional Coefficient 52

4.5.3 Example 3: Application to Mobile Manipulator 54

4.5.4 Example 4: Physical Comparative Experiments 54

4.6 Chapter Summary 57

References 57

5 Design Scheme III of FTZNN 61

5.1 Introduction 61

5.2 Problem Formulation and Neural Solver 61

5.2.1 FPZNN Model 62

5.2.2 IVP-FTZNN Model 63

5.3 Theoretical Analysis 64

5.4 Illustrative Verification 70

5.4.1 Example 1: Two-Dimensional Coefficient 70

5.4.2 Example 2: Three-Dimensional Coefficient 73

5.5 Chapter Summary 78

References 78

Part III Application to Linear Matrix Equation 81

6 Design Scheme I of FTZNN 83

6.1 Introduction 83

6.2 Convergence Speed and Robustness Co-design 84

6.3 R-FTZNN Model 90

6.3.1 Design of R-FTZNN 90

6.3.2 Analysis of R-FTZNN 91

6.4 Illustrative Verification 93

6.4.1 Numerical Example 93

6.4.2 Applications: Robotic Motion Tracking 98

6.5 Chapter Summary 101

References 102

7 Design Scheme II of FTZNN 105

7.1 Introduction 105

7.2 Problem Formulation 106

7.3 FTZNN Model 106

7.4 Theoretical Analysis 108

7.4.1 Convergence 108

7.4.2 Robustness 112

7.5 Illustrative Verification 118

7.5.1 Convergence 118

7.5.2 Robustness 121

7.6 Chapter Summary 122

References 122

Part IV Application to Optimization 125

8 FTZNN for Constrained Quadratic Programming 127

8.1 Introduction 127

8.2 Preliminaries 128

8.2.1 Problem Formulation 128

8.2.2 Optimization Theory 128

8.3 U-FTZNN Model 130