Different complex ZFs leading to different complex ZNN models for time-varying complex matrix inversion

Abstract

The Zhang neural network (ZNN), as a special class of recurrent neural network (RNN), has been proposed by Zhang et al. for the online solution of various time-varying problems. More importantly, such a ZNN is based on the Zhang function (ZF) as the error-monitoring function, which is indefinite and quite different from the usual error functions in the study of conventional algorithms, such as a scalar-valued norm-based energy function involved in the gradient-based neural network (GNN). Meanwhile, the resultant ZNN model can guarantee the global/exponential convergence performance for online time-varying problems solving by following Zhang et al.'s design method. In this paper, focusing on solving the time-varying complex matrix-inversion problem, the complex ZNN models are proposed, developed and investigated for timevarying complex matrix inversion. In addition, by introducing different complex ZFs, different corresponding complex ZNN models can be proposed and developed for time-varying complex matrix inversion. Finally, through some simulations and verifications, the illustrative results substantiate the efficacy of the complex ZNN models based on different complex ZFs for time-varying complex matrix inversion.