Extended Wang neural network for online solving a set of linear equations

Abstract

An extended Wang neural network (EWNN) is proposed to solve online a set of linear equations. Such EWNN is possessing the general nonlinear model form with redundant parts, to face existence of nonlinearity phenomena in circuit implementation of Wang neural network (WNN). Furthermore, two types of nonlinear activation are proposed for EWNN aiming to improve the convergence of the WNN. Illustrative results verify the proposed EWNN for online solving linear equations.Introduction: The problem of finding solutions of linear equations can be regarded as one fundamental issue in many engineering applications. Through large-scale analogue or digital circuits implementation, the neural network is able to solve online linear equations in a parallelprocessing manner to remedy the inefficiency of conventional numerical approaches. Wang had proposed the recurrent neural network for online solving the linear equations elegantly with a preliminary circuit implementation [1]. Raida [2] made effort to enhance the performance of such Wang neural network (WNN) by using an improved circuit schematic. Zhang and Chen [3] analysed the global exponential convergence and stability of the WNN. Chen proved the robustness of the WNN for solving linear equations with implementation noises and analysed the upper boundary of the steady-state solution error [4]. Motivation:The previous WNN was designed based on the gradientdescent approach and depicted in a linear form. However, in real circuit implementation, nonlinear phenomenon can exist in the amplifiers (which may correspond the activation-function parts of the neural network) thus the WNN is required to work under such nonlinear situation. Moreover, the neural circuit may completely break down if no redundant parts are obligated. To overcome aforementioned unexpected circumstances, an extended WNN (EWNN) is proposed to solve a set of linear equations in the Letter. By involving the ensuing proposed nonlinear activation functions, the EWNN can possess superior convergence so as to improve the convergence of the previous WNN.

Varying‐parameter finite‐time zeroing neural network for solving linear algebraic systems

“…This is due to the ease in implementability of NNs, their parallel processing capabilities, and their overall fast error convergence rates. Specifically, recurrent neural network (RNN) models are based on a vector-valued error-monitoring function [3][4][5], instead of the usually employed norm-based scalar-valued error functions [6][7][8]. A finite-time Zhang neural network (ZNN) for solving systems of linear equations, based on an efficient activation function, was proposed in [9].…”

Discrete Perturbation-Immunity Neural Network for Dynamic Constrained Redundant Robot Control

“…A class of Wang neural networks with exponential convergence is developed to settle many of the mathematical problems from the perspective of control [14]- [16] and specializes in static problems, but those problems in practice are actually dynamical, which is verified in their failure to track the theoretical solution of a dynamic problem due to the lack of velocity compensation of the dynamic parameters process [17]- [19]. In addition, the gradient neural network as a conventional recurrent neural network (RNN) based approach is employed to search the target roots of dynamic problems [20], [21].…”