Finite-Time Solution of Time-Varying Tensor Inversion by a Novel Dynamic-Parameter Zeroing Neural-Network

Time-varying tensor inversion (TVTI) problem is a kind of general time-varying inversion problem in mathematics because scalars, vectors, and matrices can all be represented by tensors. The TVTI problem is based on a novel tensor product [termed the TensorFlow (TF) product], which is extracted from the TF. For solving such a prevalent problem, the matricization of the TF product is defined, and a novel dynamic-parameter zeroing neural-network (DP-ZNN) model is proposed by combining a ZNN design formula and a dynamic-parameter. The global convergence and the upper bound of finite-time convergence of the DP-ZNN model are analyzed theoretically. For highlighting the superior convergence performance and excellent efficiency of the DP-ZNN model in solving the TVTI problem, three comparative experiments are presented in this article. Experimental results show that the DP-ZNN model has remarkable convergent speciality.

Automated summary

This article introduces the background and challenges of the time-varying tensor inversion problem, and proposes a novel DP-ZNN model to solve this problem. Through theoretical analysis and experimental verification, it is proved that the model has superior convergence performance.