A Power-Type Varying Gain Discrete-Time Recurrent Neural Network For Solving Time-Varying Linear System

Abstract Many practical engineering problems can be described as an online time-varying linear system (TVLS), and thus solving TVLS is very important in control theory and control engineering. In this paper, a novel power-type varying gain discrete-time recurrent neural network (PVG-DTRNN) is proposed to solve the TVLS problem. Compared with the state-of-art method, i.e., the fixed-parameter discrete-time zeroing neural network (FP-DTZNN), the proposed PVG-DTRNN has better convergent rate and higher accuracy. To do so, a vector error function is firstly defined. Secondly, a power-type gain implicit dynamic model is derived and needs to be further discretized. Thirdly, by using Euler forward-difference rule, a discretized dynamic model is designed. In order to get the explicit dynamic model, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is utilized to estimate the inverse of the Hessian matrix. Comparisons of computer simulations verify the effectiveness and superiority of the proposed PVG-DTRNN models.