Abstract
Recently, a special class of neural dynamics has been proposed by Zhang et al. for online solution of time-varying and/or static nonlinear equations. Different from eliminating a square-based positive error-function associated with gradient-based dynamics (GD), the design method of Zhang dynamics (ZD) is based on the elimination of an indefinite (unbounded) error-function. In this paper, for the purpose of online solution of time-varying 4th root, both continuous-time ZD (CTZD) and discrete-time ZD (DTZD) models are developed and investigated. In addition, power-sigmoid activation function is exploited in Zhang dynamics, which makes ZD models possess the property of superior convergence and better accuracy. To summarize generalization for possible widespread application, such approach is further extended to general time-varying nonlinear equations solving. Computer-simulation results demonstrate the efficacy of the ZD models for finding online time-varying 4th root and solving general time-varying equations.
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