General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations

Abstract

is article presents a general six-step discrete-time Zhang neural network (ZNN) for time-varying tensor absolute value equations. Firstly, based on the Taylor expansion theory, we derive a general Zhang et al. discretization (ZeaD) formula, i.e., a general Taylor-type 1-step-ahead numerical di erentiation rule for the rst-order derivative approximation, which contains two free parameters. Based on the bilinear transform and the Routh-Hurwitz stability criterion, the e ective domain of the two free parameters is analyzed, which can ensure the convergence of the general ZeaD formula. Secondly, based on the general ZeaD formula, we design a general six-step discrete-time ZNN (DTZNN) for time-varying tensor absolute value equations (TVTAVEs), whose steady-state residual error changes in a higher order manner than those presented in the literature. Meanwhile, the feasible region of its step size, which determines its convergence, is also studied. Finally, experiment results corroborate that the general six-step DTZNN model is quite e cient for TVTAVE solving.

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

“…In this section, two simulation examples are included to substantiate the validity and fast convergence performance of NTCTZNN (5) and NTDTZNN (13). For comparative purposes, the CTZNN model in [8] (denoted by CTZNN), the NTCTZNN in [18] (denoted by NTCTZNN-p) and NTDTZNN-p (22) are included to solve time-varying Lyapunov equation.…”

“…(2) For the constant noise, CTZNN fails We use the NTDTZNN (13) to solve this problem with constant noise n(t) = 1 or linear noise n(t) = t + 1. The numerical results are depicted in Fig.…”

“…The ZNN has been intensively studied in the literature with its increasingly applications, and many more efficient variants of ZNN have been presented. For example, for potential digital hardware realization, several multi-step discrete-time ZNNs have been designed in [10][11][12][13]. To accelerate the convergence speed of the ZNN, a super-exponential ZNN with time-varying design parameter is proposed by Chen et al [9].…”

“…Considering the linear noise n k = ak + b ∈ R n×n , the limit of the residual error e k generated by NTDTCNN(13) is O(h 2 ) if and only if the parameters γ , λ and τ satisfy…”

Noise-tolerant continuous-time Zhang neural networks for time-varying Sylvester tensor equations

“…In this paper, we are going to extend a special kind of recurrent neural networks, i.e., the continuous-time Zhang neural network (CTZNN), to solve TVSTEs. ZNN was proposed by Yunong Zhang in March 2001 [4], which is quite suitable to solve various time-varying problems, such as time-varying nonlinear optimization [28][29][30], time-varying convex quadratic programming [31], time-varying matrix pseudoinversion [32] and time-varying absolute value equations [33]. Motivated by [4,12,13], we design three noise-tolerant CTZNNs (NTCTZNN1-3) for solving TVSTEs (2).…”