Different ZFs Leading to Various ZNN Models Illustrated via Online Solution of Time-Varying Underdetermined Systems of Linear Equations with Robotic Application

Abstract

Recently, by following Zhang et al.’s design method, a special class of recurrent neural network (RNN), termed Zhang neural network (ZNN), has been proposed, generalized and investigated for solving time-varying problems. In the design procedure of ZNN models, choosing a suitable kind of error function [i.e., the so-called Zhang function (ZF) used in the methodology] plays an important role, and different ZFs may lead to various ZNN models. Besides, differing from other error functions such as nonnegative energy functions associated with the conventional gradient-based neural network (GNN), the ZF can be positive, zero, negative, bounded, or unbounded even including lower-unbounded. In this paper, different newly-designed ZNN models are proposed, developed and investigated to solve the problem of time-varying underdetermined systems of linear equations (TVUSLE) based on different ZFs. Computer-simulation results (including the robotic application of the newly-designed ZNN models) show that the effectiveness of the proposed ZNN models is well verified for solving such time-varying problems.