Robustness analysis of Wang neural network for online linear equation solving

Chen, K.

doi:10.1049/el.2012.1940

Cited by 26 publications

(12 citation statements)

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“…In general, the minimal arithmetic operations of numerical algorithms are usually proportional to the cube of the dimension of the coefficient matrix, that is, ( 3 ) [7]. In order to be satisfied with the low complexity and real-time requirements, recently, numerous novel neural networks have been exploited based on the hardware implementation [2,4,5,[8][9][10][11][12][13]. For example, Tank and Hopfield solved the linear programming problems by using their proposed Hopfield neural networks (HNN) [9], which promoted the development of the neural networks in the optimization and other application problems.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, based on the Wang neural networks [10], we present an improved gradient-based neural model for the linear simultaneous equation, and then, such neural model is applied to solve the quadratic programming with equalityconstraints. Much investigation and analysis on the Wang neural network have been presented in the previous work [10,12,13]. To make full use of the Wang neural network, we transform the convex quadratic programming into the general linear matrix-equation.…”

Section: Introductionmentioning

confidence: 99%

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Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

Chen

Zhong

2013

Journal of Applied Mathematics

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A gradient-based neural network (GNN) is improved and presented for the linear algebraic equation solving. Then, such a GNN model is used for the online solution of the convex quadratic programming (QP) with equality-constraints under the usage of Lagrangian function and Karush-Kuhn-Tucker (KKT) condition. According to the electronic architecture of such a GNN, it is known that the performance of the presented GNN could be enhanced by adopting different activation function arrays and/or design parameters. Computer simulation results substantiate that such a GNN could obtain the accurate solution of the QP problem with an effective manner.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

Chen

Zhong

2013

Journal of Applied Mathematics

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“…where x(t) ∈ R n is the neural state vector and γ is the design parameter which scales the convergence rate. According to [3,4], WNN (1) is with global (convergence) stability and robustness for disturbance noises. In this Letter, we propose the following EWNN for solving Ax = b:…”

mentioning

confidence: 99%

“…From derivation above, we can see thatv(t) ≤ 0 is negative definite. According to the well-known Lyapunov theory [4], Ax(t) can globally converge to zero. This implies that the neural state x(t) can globally converge to the theoretical solution x* of linear equations since A is nonsingular.…”

mentioning

confidence: 99%

“…For solving linear equations Ax = b with non-singular coefficient matrix A, the neural state x(t) of EWNN (2) activated by ps(3) or hs(4) activation function, can globally exponentially converge to the unique theoretical solution x* = A −1 b of the linear equations Ax = b. As compared with WNN (2), starting from the same initial state x(0), superior convergence can be achieved by EWNN (2) with ps or/and hs activation function(s).Proof: Similar as the proof of Proposition 1, we define the same Lyapunov functionv(t) =x T (t)x(t)/2.…”

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confidence: 99%

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

Zhan

Yin

2016

Electron. lett.

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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.

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An Improved Recurrent Network for Online Equality-Constrained Quadratic Programming

Chen

Zhang

2016

Advances in Brain Inspired Cognitive Systems

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Robustness analysis of Wang neural network for online linear equation solving

Cited by 26 publications

References 4 publications

Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

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

An Improved Recurrent Network for Online Equality-Constrained Quadratic Programming

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