A Neural Network for Moore—Penrose Inverse of Time-Varying Complex-Valued Matrices

Abstract

The Moore—Penrose inverse of a matrix plays a very important role in practical applications. In general, it is not easy to immediately solve the Moore—Penrose inverse of a matrix, especially for solving the Moore—Penrose inverse of a complex-valued matrix in time-varying situations. To solve this problem conveniently, in this paper, a novel Zhang neural network (ZNN) with time-varying parameter that accelerates convergence is proposed, which can solve Moore—Penrose inverse of a matrix over complex field in real time. Analysis results show that the state solutions of the proposed model can achieve super convergence in finite time with weighted sign-bi-power activation function (WSBP) and the upper bound of the convergence time is calculated. A related noise-tolerance model which possesses finite-time convergence property is proved to be more efficient in noise suppression. At last, numerical simulation illustrates the performance of the proposed model as well.