Two New Zhang Neural Networks for Solving Time-Varying Linear Equations and Inequalities Systems

Recently, Xu et al. solved a class of time-varying linear equations and inequalities systems (LEIESs) by using a Zhang neural network (ZNN) model through introducing a nonnegative relaxation vector. However, the introduction of this unknown nonnegative slack vector will increase the size and complexity of the model, thereby increasing the cost of computation. In this article, we propose two new ZNN models (called traditional Zhang neural network (TZNN) and variant Zhang neural network (VZNN) models, respectively) in which no additional relaxation vector is needed. The convergence analysis of these two new models are performed, and two simulation experiments are given to illustrate their efficiency and effectiveness for solving the time-varying LEIESs, including the applicability of our proposed models to robot manipulator.

Automated summary

In this article, two new Zhang neural network models, TZNN and VZNN, are proposed to solve time-varying linear equations and inequalities systems (LEIESs). These models do not require an additional relaxation vector, thereby reducing the computational cost. Experimental results demonstrate the efficiency and effectiveness of these models in solving LEIESs problems.