In this paper, a novel Taylor-type difference rule with $O\left({\tau }^4\right)$ pattern error is provided for the first-order derivative approximation. Then, a high accuracy noise-tolerant five-step discrete-time zeroing neural network (ZNN) (termed as FDNTZNN model) is proposed to solve the time-varying matrix inversion problem in real-time. In addition, to obtain the derivative value of time-varying variables in real-world applications, the backward-difference rule is exploited to develop the FD-NTZNN model when the derivative information is unknown (FD-NTZNN-U). Theoretical analysis demonstrates that the proposed FD-NTZNN models have the properties of 0$-$stability, consistency and convergence. For comparative analysis, the classical Euler-type discrete-time ZNN model (EDZNN), five-step Taylor-type discrete-time ZNN model (FDZNN) and Euler-type discrete-time noise-tolerant ZNN (NTZNN) model (ED-NTZNN) are reconsidered. Ultimately, two illustrative numerical simulations and an application example to motion generation of manipulator are simulated to substantiate the feasibility and effectiveness of the proposed FD-NTZNN model and FD-NTZNN-U model for online time-varying matrix inversion in the presence of different types of noise.

本文提出了一种新的泰勒型差分法则 $Ø（{\tau }^4）$为一阶导数逼近提供了模式误差。然后，提出了一种高精度的耐噪声五步离散时间归零神经网络（ZNN）（称为FDNTZNN模型），以实时解决时变矩阵求逆问题。另外，为了获得现实应用中时变变量的导数值，当导数信息未知时，利用后向差分规则建立FD-NTZNN模型（FD-NTZNN-U）。理论分析表明，所提出的FD-NTZNN模型具有0的性质$-$稳定性，一致性和收敛性。为了进行比较分析，可以使用经典的Euler型离散时间ZNN模型（EDZNN），五步Taylor型离散时间ZNN模型（FDZNN）和Euler型离散时间耐噪声ZNN模型（ED-NN NTZNN）。最终，通过两个示例性数值模拟和一个机械手运动产生的应用实例，以验证所提出的FD-NTZNN模型和FD-NTZNN-U模型在存在不同类型时进行在线时变矩阵求逆的可行性和有效性。的噪音。