A Noise-Tolerant Zeroing Neural Network for Time-Dependent Complex Matrix Inversion Under Various Kinds of Noises

Abstract

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this study, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models.

A Fully Complex-Valued and Robust ZNN Model for Dynamic Complex Matrix Inversion Under External Noises

“…In this article, the goal is to solve Z(t) from (1) by proposing a fully complex-valued and robust zeroing neural network (CVRZNN) model under various kinds of external noises. Compared with the neural model proposed in [34], the CVRZNN model does not process the real and imaginary parts of the complex matrix separately, while the complex matrix is treated as a whole to be discussed and analyzed.…”

“…Furthermore, external noises are considered in the complex-valued problems. For example, in [34], Xiao et al propose a noise tolerant ZNN model for solving time-varying complex matrix problem under various kinds of noises, which adopts the first method to solve complex-valued problem and time complexity and space complexity are increased. Therefore, in order to reduce the computation complexity and suppress external disturbances, a fully complex-valued and robust zeroing neural network (CVRZNN) model is designed by using the second method to solve the complex-valued matrix inversion problem under various external noises.…”

“…• A novel fully complex-valued and robust zeroing neural network (CVRZNN) model is proposed to solve dynamic matrix inversion with various types of noises. The CVRZNN model can directly find the accurate inversion of complex matrix without extra transformation, and greatly increase the computational efficiency, as compared to the handling process of [34].…”

Noise-Tolerant Zeroing Neural Dynamics for Solving Hybrid Multilayered Time-Varying Linear Equation System

“…TVLES, which originates from time-invariant linear equation system, has been investigated [24][25][26][27][28]. Zeroing neural dynamics (ZND) method is a good alternative for solving TVLES [11,21,[27][28][29][30][31][32][33][34][35]. ZND is also called Zhang neural dynamics and Zhang neural network, which is a special class of recurrent neural network and originates from Hoefeld neural network [21,27,28].…”

Finite-Time Convergence and Robustness Analysis of Two Nonlinear Activated ZNN Models for Time-Varying Linear Matrix Equations

“…[23] has briefly reviewed how to design continuous-time ZNN models meeting with different problems. Considering the characters of convergence rate and robustness, the activation functions [24]- [26] are usually added into ZNN models. For further study, Li et al [27] proposed a nonlinear activation function which can realize finite-time convergence of ZNN models.…”