Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

中文翻译：

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新型机器人机械臂离散时间递归神经网络：直接离散化技术路线


时变问题的控制和处理在工程和科学领域具有普遍性，离散时间递归神经网络（RNN）模型已被证明是处理各种离散时变问题的有效方法。但此类模型通常源于连续时变问题的离散化研究，而直接离散化方法的研究较少。为了解决上述问题，本文提出了一种新颖的离散时间 RNN 模型，开创性地解决离散时变问题。具体而言，提出了源自串行机器人机械臂数学建模的离散时变非线性系统作为目标问题。为了解决该问题，首先采用二阶泰勒展开技术来处理离散时变非线性系统，随后提出了新颖的离散时间RNN模型。其次，研究和发展了理论分析，证明了所提出的离散时间 RNN 模型的收敛性和精度。此外，三个不同的数值实验验证了所提出的离散时间 RNN 模型的优异性能。此外，机器人机械手的例子进一步验证了所提出的新型离散时间RNN模型的有效性和实用性。