Zeroing Neural Network With Coefficient Functions and Adjustable Parameters for Solving Time-Variant Sylvester Equation

MNTZNN for Solving Hybrid Double-Deck Dynamic Nonlinear Equation System Applied to Robot Manipulator Control

Compared with conventional dynamic nonlinear equation systems, a hybrid double-deck dynamic nonlinear equation system (H3DNES) not only has multiple layers describing more different tasks in practice, but also has a hybrid nonlinear structure of solution and its derivative describing their nonlinear constraints. Its characteristics lead to the ability to describe more complicated problems involving multiple constraints, and strong nonlinear and dynamic features, such as robot manipulator tracking control. Besides, noises are inevitable in practice and thus strong robustness of models solving H3DNES is also necessary. In this work, a multilayered noise-tolerant zeroing neural network (MNTZNN) model is proposed for solving H3DNES. MNTZNN model has strong robustness and it solves H3DNES successfully even when noises exist in both the two layers of H3DNES. In order to develop the MNTZNN model, a new zeroing neural network (ZNN) design formula is proposed. It not only enables equations with respect to solutions to become equations with respect to the second-order derivatives of solutions but also makes the corresponding model have strong robustness. The robustness of the MNTZNN model is proved when parameters in the model satisfy a loose constraint and the error bounds are programmable via setting appropriate parameter values. Finally, the MNTZNN model is applied to the tracking control of the six-link planar robot manipulator and PUMA560 robot manipulator with hybrid nonlinear constraints of joint angle and velocity.

Novel adaptive zeroing neural dynamics schemes for temporally-varying linear equation handling applied to arm path following and target motion positioning

While the handling for temporally-varying linear equation (TVLE) has received extensive attention, most methods focused on trading off the conflict between computational precision and convergence rate. Different from previous studies, this paper proposes two complete adaptive zeroing neural dynamics (ZND) schemes, including a novel adaptive continuous ZND (ACZND) model, two general variable time discretization techniques, and two resultant adaptive discrete ZND (ADZND) algorithms, to essentially eliminate the conflict. Specifically, an error-related varying-parameter ACZND model with global and exponential convergence is first designed and proposed. To further adapt to the digital hardware, two novel variable time discretization techniques are proposed to discretize the ACZND model into two ADZND algorithms. The convergence properties with respect to the convergence rate and precision of ADZND algorithms are proved via rigorous mathematical analyses. By comparing with the traditional discrete ZND (TDZND) algorithms, the superiority of ADZND algorithms in convergence rate and computational precision is shown theoretically and experimentally. Finally, simulative experiments, including numerical experiments on a specific TVLE solving as well as four application experiments on arm path following and target motion positioning are successfully conducted to substantiate the efficacy, superiority, and practicability of ADZND algorithms.