PNSND: A Novel Solution for Dynamic Nonlinear Equations and Its Application to Robotic Arm

Dynamic nonlinear equations (DNEs) are essential for modeling complex systems in various fields due to their ability to capture real-world phenomena. However, the solution of DNEs presents significant challenges, especially in industrial settings where periodic noise often compromises solution fidelity. To tackle this challenge, we propose a novel approach called Periodic Noise Suppression Neural Dynamic (PNSND), which leverages the gradient descent approach and incorporates velocity compensation to overcome the limitations of the traditional Gradient Neural Dynamic (GND) model. Additionally, the PNSND model aims to suppress periodic noise by addressing its harmonic properties according to the method of Fourier decomposition of harmonics. In the paper, we explore the performance of convergence and robustness of the PNSND model. Moreover, we demonstrate the effectiveness of the PNSND model in addressing dynamic nonlinear problems under periodic noise interference through its application to robotic arm, highlighting its practical significance in industrial contexts.

动态非线性方程（DNEs）在诸多领域内对复杂系统的建模至关重要，因其具备捕捉现实世界现象的能力。然而，DNEs的求解过程面临着巨大的挑战，尤其是在工业环境中，周期性噪声常常导致求解精度受损。为应对这一挑战，本文提出了一种名为周期噪声抑制神经动态（PNSND）的创新方法，该方法利用梯度下降法，并引入速度补偿以克服传统梯度神经动态（GND）模型的局限性。此外，PNSND模型旨在通过傅里叶谐波分解的方法，针对周期噪声的谐波特性进行抑制。在论文中，我们探讨了PNSND模型的收敛性能与鲁棒性。同时，我们通过将PNSND模型应用于机器人臂的动态非线性问题中，以克服周期噪声干扰，展示了其在工业环境中的实际应用效果，从而凸显了其在工业场景中的实践意义。