An exponential-enhanced-type varying-parameter RNN for solving time-varying matrix inversion

Abstract

In order to compute time-varying matrix inversion faster, a novel exponential-enhanced-type varying-parameter recurrent neural network (EVP-RNN) is proposed and investigated in this paper. First, the detailed design process of the proposed EVP-RNN is stated and presented. Then, mathematical analysis proves that the proposed EVP-RNN has superior exponential convergence property than the conventional fixed-parameter recurrent neural network (FP-RNN) with four kinds of specific activation functions. Meanwhile, the guideline of choosing an activation function is provided to achieve a better convergence property. Third, theoretical analysis shows that the upper-bounds of calculation error of EVP-RNN are always smaller than those of FP-RNN and actual calculation error of EVP-RNN always converges faster than that of the FP-RNN. Simultaneously, an idea of designing a time-varying parameter is given. Finally, the results of comparative simulations verify the effectiveness, high accuracy, and superiority of the EVP-RNN compared with the traditional FP-RNN for solving time-varying matrix inversion.