Convergence and stability results of Zhang neural network solving systems of time-varying nonlinear equations

Abstract

For solving systems of time-varying nonlinear equations, this paper generalizes a special kind of recurrent neural network by using a design method proposed by Zhang et al. Such a recurrent neural network (termed Zhang neural network, ZNN) is designed based on an indefinite error-function instead of a norm-based energy function. Theoretical analysis and results of convergence and stability are presented to show the desirable properties (e.g., large-scale exponential convergence) of ZNN via two different activation-function arrays for solving systems of time-varying nonlinear equations. Computer-simulation results substantiate further the theoretical analysis and efficacy of ZNN for solving systems of time-varying nonlinear equations.

Broyden-Method Aided Discrete ZNN Solving the Systems of Time-Varying Nonlinear Equations

“…Choice of the activation function array Φ(·) determines the type of convergence. It has been proved that an STVNE-solving continuous ZNN model with linear activation function Φ(·) possesses exponential convergence [5]. There are also other kinds of suitable Φ(·) which can produce better convergence performance [5]; but, for analytical convenience, this paper uses only the linear array…”

“…Zhang neural network (ZNN) is an efficient continuous model for solving dynamical problems [2]- [4], and has been proved to be able to solve systems of time-varying nonlinear equations (STVNE) with exponential convergence rate [5]. For numerical implementation, the STVNE-solving continuous ZNN is discretized into two discrete models: DZ-K (discrete ZNN with the system's time-derivative information f t known) and DZ-U (discrete ZNN with the system's timederivative information f t unknown).…”