Zeroing dynamics, gradient dynamics, and Newton iterations. (2016)

• Record Type: Book
• Further Information: Note: Yunong Zhang, Lin Xiao, Zhengli Xiao, Mingzhi Mao.
• Authors: Zhang, Yunong; Xiao, Lin, 1972-; Xiao, Zhengli; Mao, Mingzhi
• Contents: Time-Varying Root Finding; Time-Varying Square Root Finding; Introduction; Problem Formulation and Continuous-Time (CT) Models; S-DTZD Model and Newton Iteration; Illustrative Examples Time-Varying Cube Root Finding; Introduction; ZD Models for Time-Varying Case; Simplified ZD Models for Constant Case and Newton Iteration; Illustrative Examples Time-Varying 4 th Root Finding; Introduction; Problem Formulation and ZD Models; GD Model; Illustrative Examples Time-Varying 5 th Root Finding; Introduction; ZD Models for Time-Varying Case; Simplified ZD Models for Constant Case and Newton Iteration; Illustrative Examples; Appendix: Extension to Time-Varying p th Root Finding Nonlinear Equation Solving ; Time-Varying Nonlinear Equation Solving; Introduction; Problem Formulation and Solution Models; Convergence Analysis; Illustrative Example Static Nonlinear Equation Solving; Problem Formulation and Continuous-Time Models; DTZD Models; Comparison between CTZD Model and Newton Iteration; Further Discussion to Avoid Local Minimum System of Nonlinear Equations Solving; Problem Formulation and CTZD Model; Discrete-Time Models Matrix Inversion; ZD Models and Newton Iteration; Introduction; ZD Models; Choices of Initial State X 0 ; Choices of Step Size h ; Illustrative Examples; New DTZD Models Aided with Line-Search Algorithm Moore–Penrose Inversion; Introduction; Preliminaries; ZD Models for Moore–Penrose Inverse; Comparison between ZD and GD Models; Simulation and Verification; Application to Robot Arm Matrix Square Root Finding ; ZD Models and Newton Iteration; Introduction; Problem Formulation and ZD Models; Link and Explanation to Newton Iteration; Line-Search Algorithm; Illustrative Examples ZD Model Using Hyperbolic Sine Activation Functions; Model and Activation Functions; Convergence Analysis; Robustness Analysis; Illustrative Examples Time-Varying Quadratic Optimization ; ZD Models for Quadratic Minimization; Introduction; Problem Formulation and CTZD Model; DTZD Models; GD Models; Illustrative Example ZD Models for Quadratic Programming; Introduction; CTZD Model; DTZD Models; Illustrative Examples Simulative and Experimental Application to Robot Arms; Problem Formulation and Reformulation; Solution Models; Computer Simulations; Hardware Experiments Time-Varying Inequality Solving ; Linear Inequality Solving ; Introduction; Time-Varying Linear Inequality; Constant Linear Inequality; Illustrative Examples ; System of Time-Varying Linear Inequalities; Illustrative Examples System of Time-Varying Nonlinear Inequalities Solving; Introduction; Problem Formulation; CZD Model and Convergence Analysis; MZD Model and Convergence Analysis; Illustrative Example Application to Fractal; Fractals Yielded via Static Nonlinear Equation; Introduction; Complex-Valued ZD Models; Illustrative Examples Fractals Yielded via Time-Varying Nonlinear Equation; Introduction; Complex-Valued ZD Models; Illustrative Examples A summary appears at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 003.83; Discrete-time systems; Neural networks (Computer science)
• Languages: English
• ISBNs: 9781498753784; 9781498753791
• Related ISBNs: 9781498753760
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.