Different Zhang functions leading to different ZNN models illustrated via time-varying matrix square roots finding

Authors:
Yunong Zhang;Weibing Li;Dongsheng Guo;Zhende Ke
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, PR China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, PR China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, PR China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, PR China
Venue:
Expert Systems with Applications: An International Journal
Year:
2013

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Abstract

In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online nonlinear matrix equation problems. Recently, a novel class of neural networks, termed Zhang neural network (ZNN), has been formally proposed by Zhang et al. for solving online time-varying problems. Such a neural-dynamic system is elegantly designed by defining an indefinite matrix-valued error-monitoring function, which is called Zhang function (ZF). The dynamical system is then cast in the form of a first-order differential equation by using matrix notation. In this paper, different indefinite ZFs, which lead to different ZNN models, are proposed and developed as the error-monitoring functions for time-varying matrix square roots finding. Towards the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modeling and verifications of such ZNN models are further investigated for online solution of time-varying matrix square roots. Both theoretical analysis and modeling results substantiate the efficacy of the proposed ZNN models for time-varying matrix square roots finding.