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.

中文翻译：

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动态非线性方程组求解的新型离散递归神经网络设计，验证与应用

最近，基于递归神经网络（RNN）的方法已被认为是解决数学问题的有力替代方法。在这项研究中，提出并研究了一种新的离散时间RNN（DTRNN），以确定动态非线性方程的精确解。具体而言，通过使用泰勒型差分规则，建立了最终的DTRNN模型，用于求解动态非线性方程。然后从理论上证明了该DTRNN模型具有$ O（\ tau ^ 4）$ 错误模式，其中 $ \ tau $表示采样间隙。说明了比较数值结果，以进一步证实所提出的DTRNN模型与现有方法相比的有效性和优越性。最后，通过求解动态非线性运动方程组，将所提出的DTRNN模型应用于冗余机器人操纵器，说明了该模型的应用前景。