A new recurrent neural network based on direct discretization method for solving discrete time-variant matrix inversion with application

In recent years, many researchers have worked hard to find a better way for solving discrete time-variant problems in industrial control science and automation. For example, some researchers propose RNN models to deal with such problems. Typical discrete time-variant problems, such as discrete time-variant matrix inversion, are developed from continuous time-variant problems. In the present paper, an efficient and straightforward method is proposed to solve discrete time-variant matrix inversion, note that it can skip the solving procedures of continuous time-variant problem and solves matrix inversion directly in the discrete time-variant environment. Specifically, an innovative discrete time-variant recurrent neural network (I-DT-RNN) model for dealing with discrete time-variant matrix inversion is proposed, furthermore it is mathematically founded on the second-order Taylor expansion. The theoretical analysis results of I-DT-RNN model are also presented, which proves that the proposed I-DT-RNN model has a reasonable characteristic and also shows that the proposed I-DT-RNN model has an excellent computational performance. Moreover, in the numerical experiments part, we present three different matrices as numerical experiment examples and an application of two-link robot manipulator as an industrial example for validating the practicability of the I-DT-RNN model.