An advanced discrete-time RNN for handling discrete time-varying matrix inversion: Form model design to disturbance-suppression analysis

Abstract

Time-varying matrix inversion is an important field of matrix research, and lots of research achievements have been obtained. In the process of solving time-varying matrix inversion, disturbances inevitably exist, thus, a model that can suppress disturbance while solving the problem is required. In this paper, an advanced continuous-time recurrent neural network (RNN) model based on a double integral RNN design formula is proposed for solving continuous time-varying matrix inversion, which has incomparable disturbance-suppression property. For digital hardware applications, the corresponding advanced discrete-time RNN model is proposed based on the discretisation formulas. As a result of theoretical analysis, it is demonstrated that the advanced continuous-time RNN model and the corresponding advanced discrete-time RNN model have global and exponential convergence performance, and they are excellent for suppressing different disturbances. Finally, inspiring experiments, including two numerical experiments and a practical experiment, are presented to demonstrate the effectiveness and superiority of the advanced discrete-time RNN model for solving discrete time-varying matrix inversion with disturbance-suppression.