Zeroing dynamics, gradient dynamics, and Newton iterations

Content: 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 4th Root Finding Introduction Problem Formulation and ZD Models GD Model Illustrative Examples Time-Varying 5th 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 pth 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 X0 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 VerificationApplication 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 IntroductionTime-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 ExamplesA summary appears at the end of each chapter.