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Zeroing Neural Networks : Finite-Time Convergence Design, Analysis and Applications /

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 theor...

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Bibliographic Details
Main Author: Xiao, Lin, 1972-
Other Authors: Jia, Lei
Format: eBook
Language:English
Published: Newark : John Wiley & Sons, Incorporated, 2022.
Subjects:
Neural networks (Computer science)
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • List of Figures
  • List of Tables
  • Author Biographies
  • Preface
  • Acknowledgments
  • Part I Application to Matrix Square Root
  • Chapter 1 FTZNN for Time-varying Matrix Square Root
  • 1.1 Introduction
  • 1.2 Problem Formulation and ZNN Model
  • 1.3 FTZNN Model
  • 1.3.1 Model Design
  • 1.3.2 Theoretical Analysis
  • 1.4 Illustrative Verification
  • 1.5 Chapter Summary
  • References
  • Chapter 2 FTZNN for Static Matrix Square Root
  • 2.1 Introduction
  • 2.2 Solution Models
  • 2.2.1 OZNN Model
  • 2.2.2 FTZNN Model
  • 2.3 Illustrative Verification
  • 2.3.1 Example 1
  • 2.3.2 Example 2
  • 2.4 Chapter Summary
  • References
  • Part II Application to Matrix Inversion
  • Chapter 3 Design Scheme I of FTZNN
  • 3.1 Introduction
  • 3.2 Problem Formulation and Preliminaries
  • 3.3 FTZNN Model
  • 3.3.1 Model Design
  • 3.3.2 Theoretical Analysis
  • 3.4 Illustrative Verification
  • 3.4.1 Example 1: Nonrandom Time-varying Coefficients
  • 3.4.2 Example 2: Random Time-varying Coefficients
  • 3.5 Chapter Summary
  • References
  • Chapter 4 Design Scheme II of FTZNN
  • 4.1 Introduction
  • 4.2 Preliminaries
  • 4.2.1 Mathematical Preparation
  • 4.2.2 Problem Formulation
  • 4.3 NT-FTZNN Model
  • 4.4 Theoretical Analysis
  • 4.4.1 NT-FTZNN in the Absence of Noises
  • 4.4.2 NT-FTZNN in the Presence of Noises
  • 4.4.2.1 Dynamic Bounded Gradually Disappearing Noise
  • 4.4.2.2 Dynamic Bounded Non-disappearing Noise
  • 4.5 Illustrative Verification
  • 4.5.1 Example 1: Two-dimensional Coefficient
  • 4.5.2 Example 2: Six-dimensional Coefficient
  • 4.5.3 Example 3: Application to Mobile Manipulator
  • 4.5.4 Example 4: Physical Comparative Experiments
  • 4.6 Chapter Summary
  • References
  • Chapter 5 Design Scheme III of FTZNN
  • 5.1 Introduction
  • 5.2 Problem Formulation and Neural Solver
  • 5.2.1 FPZNN Model.
  • 5.2.2 IVP-FTZNN Model
  • 5.3 Theoretical Analysis
  • 5.4 Illustrative Verification
  • 5.4.1 Example 1: Two-Dimensional Coefficient
  • 5.4.2 Example 2: Three-Dimensional Coefficient
  • 5.5 Chapter Summary
  • References
  • Part III Application to Linear Matrix Equation
  • Chapter 6 Design Scheme I of FTZNN
  • 6.1 Introduction
  • 6.2 Convergence Speed and Robustness Co-design
  • 6.3 R-FTZNN Model
  • 6.3.1 Design of R-FTZNN
  • 6.3.2 Analysis of R-FTZNN
  • 6.4 Illustrative Verification
  • 6.4.1 Numerical Example
  • 6.4.1.1 No Noise Considered
  • 6.4.1.2 With Noises Considered
  • 6.4.2 Applications: Robotic Motion Tracking
  • 6.5 Chapter Summary
  • References
  • Chapter 7 Design Scheme II of FTZNN
  • 7.1 Introduction
  • 7.2 Problem Formulation
  • 7.3 FTZNN Model
  • 7.4 Theoretical Analysis
  • 7.4.1 Convergence
  • 7.4.2 Robustness
  • 7.5 Illustrative Verification
  • 7.5.1 Convergence
  • 7.5.2 Robustness
  • 7.6 Chapter Summary
  • References
  • Part IV Application to Optimization
  • Chapter 8 FTZNN for Constrained Quadratic Programming
  • 8.1 Introduction
  • 8.2 Preliminaries
  • 8.2.1 Problem Formulation
  • 8.2.2 Optimization Theory
  • 8.3 U-FTZNN Model
  • 8.4 Convergence Analysis
  • 8.5 Robustness Analysis
  • 8.6 Illustrative Verification
  • 8.6.1 Qualitative Experiments
  • 8.6.2 Quantitative Experiments
  • 8.7 Application to Image Fusion
  • 8.8 Application to Robot Control
  • 8.9 Chapter Summary
  • References
  • Chapter 9 FTZNN for Nonlinear Minimization
  • 9.1 Introduction
  • 9.2 Problem Formulation and ZNN Models
  • 9.2.1 Problem Formulation
  • 9.2.2 ZNN Model
  • 9.2.3 RZNN Model
  • 9.3 Design and Analysis of R-FTZNN
  • 9.3.1 Second-Order Nonlinear Formula
  • 9.3.2 R-FTZNN Model
  • 9.4 Illustrative Verification
  • 9.4.1 Constant Noise
  • 9.4.2 Dynamic Noise
  • 9.5 Chapter Summary
  • References
  • Chapter 10 FTZNN for Quadratic Optimization.
  • 10.1 Introduction
  • 10.2 Problem Formulation
  • 10.3 Related Work: GNN and ZNN Models
  • 10.3.1 GNN Model
  • 10.3.2 ZNN Model
  • 10.4 N-FTZNN Model
  • 10.4.1 Models Comparison
  • 10.4.2 Finite-Time Convergence
  • 10.5 Illustrative Verification
  • 10.6 Chapter Summary
  • References
  • Part V Application to the Lyapunov Equation
  • Chapter 11 Design Scheme I of FTZNN
  • 11.1 Introduction
  • 11.2 Problem Formulation and Related Work
  • 11.2.1 GNN Model
  • 11.2.2 ZNN Model
  • 11.3 FTZNN Model
  • 11.4 Illustrative Verification
  • 11.5 Chapter Summary
  • References
  • Chapter 12 Design Scheme II of FTZNN
  • 12.1 Introduction
  • 12.2 Problem Formulation and Preliminaries
  • 12.3 FTZNN Model
  • 12.3.1 Design of FTZNN
  • 12.3.2 Analysis of FTZNN
  • 12.4 Illustrative Verification
  • 12.5 Application to Tracking Control
  • 12.6 Chapter Summary
  • References
  • Chapter 13 Design Scheme III of FTZNN
  • 13.1 Introduction
  • 13.2 N-FTZNN Model
  • 13.2.1 Design of N-FTZNN
  • 13.2.2 Re-Interpretation from Nonlinear PID Perspective
  • 13.3 Theoretical Analysis
  • 13.4 Illustrative Verification
  • 13.4.1 Numerical Comparison
  • 13.4.2 Application Comparison
  • 13.4.3 Experimental Verification
  • 13.5 Chapter Summary
  • References
  • Part VI Application to the Sylvester Equation
  • Chapter 14 Design Scheme I of FTZNN
  • 14.1 Introduction
  • 14.2 Problem Formulation and ZNN Model
  • 14.3 N-FTZNN Model
  • 14.3.1 Design of N-FTZNN
  • 14.3.2 Theoretical Analysis
  • 14.4 Illustrative Verification
  • 14.5 Robotic Application
  • 14.6 Chapter Summary
  • References
  • Chapter 15 Design Scheme II of FTZNN
  • 15.1 Introduction
  • 15.2 ZNN Model and Activation Functions
  • 15.2.1 ZNN Model
  • 15.2.2 Commonly Used AFs
  • 15.2.3 Two Novel Nonlinear AFs
  • 15.3 NT-PTZNN Models and Theoretical Analysis
  • 15.3.1 NT-PTZNN1 Model
  • 15.3.1.1 Case 1
  • 15.3.1.2 Case 2.
  • 15.3.2 NT-PTZNN2 Model
  • 15.3.2.1 Case 1
  • 15.3.2.2 Case 2
  • 15.4 Illustrative Verification
  • 15.4.1 Example 1
  • 15.4.2 Example 2
  • 15.4.3 Example 3
  • 15.5 Chapter Summary
  • References
  • Chapter 16 Design Scheme III of FTZNN
  • 16.1 Introduction
  • 16.2 ZNN Model and Activation Function
  • 16.2.1 ZNN Model
  • 16.2.2 Sign-bi-power Activation Function
  • 16.3 FTZNN Models with Adaptive Coefficients
  • 16.3.1 SA-FTZNN Model
  • 16.3.2 PA-FTZNN Model
  • 16.3.3 EA-FTZNN Model
  • 16.4 Illustrative Verification
  • 16.5 Chapter Summary
  • References
  • Part VII Application to Inequality
  • Chapter 17 Design Scheme I of FTZNN
  • 17.1 Introduction
  • 17.2 FTZNN Models Design
  • 17.2.1 Problem Formulation
  • 17.2.2 ZNN Model
  • 17.2.3 Vectorization
  • 17.2.4 Activation Functions
  • 17.2.5 FTZNN Models
  • 17.3 Theoretical Analysis
  • 17.3.1 Global Convergence
  • 17.3.2 Finite-Time Convergence
  • 17.4 Illustrative Verification
  • 17.5 Chapter Summary
  • References
  • Chapter 18 Design Scheme II of FTZNN
  • 18.1 Introduction
  • 18.2 NT-FTZNN Model Deisgn
  • 18.2.1 Problem Formulation
  • 18.2.2 ZNN Model
  • 18.2.3 NT-FTZNN Model
  • 18.2.4 Activation Functions
  • 18.3 Theoretical Analysis
  • 18.3.1 Global Convergence
  • 18.3.2 Finite-Time Convergence
  • 18.3.3 Noise-Tolerant Convergence
  • 18.4 Illustrative Verification
  • 18.5 Chapter Summary
  • References
  • Part VIII Application to Nonlinear Equation
  • Chapter 19 Design Scheme I of FTZNN
  • 19.1 Introduction
  • 19.2 Model Formulation
  • 19.2.1 OZNN Model
  • 19.2.2 FTZNN Model
  • 19.2.3 Models Comparison
  • 19.3 Convergence Analysis
  • 19.4 Illustrative Verification
  • 19.4.1 Nonlinear Equation f(u) with Simple Root
  • 19.4.2 Nonlinear Equation f(u) with Multiple Root
  • 19.5 Chapter Summary
  • References
  • Chapter 20 Design Scheme II of FTZNN
  • 20.1 Introduction
  • 20.2 Problem and Model Formulation.
  • 20.2.1 GNN Model
  • 20.2.2 OZNN Model
  • 20.3 FTZNN Model and Finite-Time Convergence
  • 20.4 Illustrative Verification
  • 20.5 Chapter Summary
  • References
  • Chapter 21 Design Scheme III of FTZNN
  • 21.1 Introduction
  • 21.2 Problem Formulation and ZNN Models
  • 21.2.1 Problem Formulation
  • 21.2.2 ZNN Model
  • 21.3 Robust and Fixed-Time ZNN Model
  • 21.4 Theoretical Analysis
  • 21.4.1 Case 1: No Noise
  • 21.4.2 Case 2: Under External Noises
  • 21.5 Illustrative Verification
  • 21.6 Chapter Summary
  • References
  • Index
  • EULA.