Different Zhang functions leading to various ZNN models illustrated via solving the time-varying overdetermined system of linear equations

Since 2001, a special class of recurrent neural network (RNN), termed Zhang neural network (ZNN), has been proposed, generalized and investigated for solving time-varying problems by following Zhang et al.´s design method. In the procedure of constructing ZNN models, designing a suitable error function [i.e., the so-called Zhang function (ZF) used in the methodology] plays an important role, as different ZFs lead to various ZNN models. Besides, differing from other error functions, e.g., the nonnegative energy function associated with the conventional gradient-based neural network (GNN), ZF is indefinite which means that such a ZF can be positive, zero, negative, bounded, or unbounded, even lower-unbounded. In this paper, two different main ZNN models are designed, constructed and investigated to solve the problem of time-varying overdetermined system of linear equations (TVOSLE) by exploiting different ZFs. Computer-simulation results substantiate the effectiveness of the two main ZNN models for solving such a time-varying problem.