This research first proposes the general expression of Zhang et al. discretization (ZeaD) formulas to provide an effective general framework for finding various ZeaD formulas by the idea of high-order derivative simultaneous elimination. Then, to solve the problem of future equality-constrained nonlinear optimization (ECNO) with various noises, a specific ZeaD formula originating from the general ZeaD formula is further studied for the discretization of a noise-perturbed continuous-time advanced zeroing neurodynamic model. Subsequently, the resulting noise-perturbed discrete-time advanced zeroing neurodynamic (NP-DTAZN) algorithm is proposed for the real-time solution to the future ECNO problem with various noises suppressed simultaneously. Moreover, theoretical and numerical results are presented to show the convergence and precision of the proposed NP-DTAZN algorithm in the perturbation of various noises. Finally, comparative numerical and physical experiments based on a Kinova JACO ² robot manipulator are conducted to further substantiate the efficacy, superiority, and practicability of the proposed NP-DTAZN algorithm for solving the future ECNO problem with various noises.

中文翻译：

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离散时间高级归零神经动力学算法应用于未来具有各种噪声的等式约束非线性优化

本研究首先提出张的一般表达等。离散化（ZeaD）公式，通过高阶导数同时消除的思想，为寻找各种 ZeaD 公式提供了一个有效的通用框架。然后，为了解决未来具有各种噪声的等式约束非线性优化（ECNO）问题，进一步研究了源自一般 ZeaD 公式的特定 ZeaD 公式，用于离散化噪声扰动的连续时间高级归零神经动力学模型。随后，提出了由此产生的噪声扰动离散时间高级归零神经动力学（NP-DTAZN）算法，用于实时解决未来的ECNO问题，同时抑制各种噪声。此外，理论和数值结果表明了所提出的NP-DTAZN算法在各种噪声扰动下的收敛性和精度。 ²机器人机械手进一步证实了所提出的NP-DTAZN算法在解决未来具有各种噪声的ECNO问题中的有效性、优越性和实用性。