Continuous and discrete gradient-Zhang neuronet (GZN) with analyses for time-variant overdetermined linear equation system solving as well as mobile localization applications

Abstract

In this paper, a novel continuous gradient-Zhang neuronet (GZN) model and three discrete GZN algorithms are proposed to solve time-variant overdetermined linear equation system (TVOLES) problems, and are developed on the basis of a gradient neuronet and Zhang neuronet. Specifically, the continuous GZN model is proposed and derived in the form of an explicit-dynamic equation, and its stability is analysed and proven using Lyapunov theory. To ensure that the problems can be solved and implemented on digital platforms, three discrete GZN algorithms are established by using three different discretization formulas. The numerical simulative results verify that, compared with the Zhang neuronet model, gradient neuronet model and variant-parameter neuronet model, the proposed continuous GZN model converges faster in some cases. Other computer experiments further substantiate that the proposed continuous model and its corresponding discrete GZN algorithms are effective and efficient. Finally, the proposed discrete GZN algorithms are applied to mobile object localizations, and the simulative results verify their applicability and effectiveness.