Different ZFs leading to various ZNN models illustrated via online solution of time-varying underdetermined systems of linear equations with robotic application

Authors:
Yunong Zhang;Ying Wang;Long Jin;Bingguo Mu;Huicheng Zheng
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China
Venue:
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part II
Year:
2013

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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.