RNN Models for Dynamic Matrix Inversion: A Control-Theoretical Perspective

In this paper, the existing recurrent neural network (RNN) models for solving zero-finding (e.g., matrix inversion) with time-varying parameters are revisited from the perspective of control and unified into a control-theoretical framework. Then, limitations on the activated functions of existing RNN models are pointed out and remedied with the aid of control-theoretical techniques. In addition, gradient-based RNNs, as the classical method for zero-finding, have been remolded to solve dynamic problems in manners free of errors and matrix inversions. Finally, computer simulations are conducted and analyzed to illustrate the efficacy and superiority of the modified RNN models designed from the perspective of control. The main contribution of this paper lies in the removal of the convex restriction and the elimination of the matrix inversion in existing RNN models for the dynamic matrix inversion. This work provides a systematic approach on exploiting control techniques to design RNN models for robustly and accurately solving algebraic equations.