Design, Verification, and Application of New Discrete-Time Recurrent Neural Network for Dynamic Nonlinear Equations Solving

Abstract

Recently, the approach based on recurrent neural network (RNN) has been considered a powerful alternative to mathematical problem solving. In this study, a new discrete-time RNN (DTRNN) is proposed and investigated to determine an exact solution of dynamic nonlinear equations. Specifically, the resultant DTRNN model is established for solving dynamic nonlinear equations by utilizing a Taylor-type difference rule. This DTRNN model is then theoretically proven to have an $O(\tau ^4)$ error pattern, where $\tau$ denotes the sampling gap. Comparative numerical results are illustrated to further substantiate the efficacy and superiority of the proposed DTRNN model in comparison with the existing approach. Finally, the proposed DTRNN model is applied to redundant robot manipulators by solving the system of dynamic nonlinear kinematic equations, indicating the application prospect of the proposed model.