As a classical and effective method for solving various time-varying problems, the zeroing neural network (ZNN) is widely applied in the scientific and industrial realms. In plentiful studies on the ZNN model, its robustness and convergence have been two essential criteria to evaluate the quality of the model. Improvements in the ZNN model have been focused on its convergence speed; however, the adjustability of its convergence speed has been neglected in most prior works, which restricts its extensive promotion in practical application. Considering the above-mentioned issue, a well-designed activation function (WDAF) is designed. Based on the WDAF, a robust predefined-time convergence ZNN (RPTCZNN) model with adjustable convergence speed is proposed to solve the dynamic matrix inversion problem. In addition, the upper bound of the RPTCZNN model’s convergence time is theoretically validated by strict mathematical analysis in a noiseless and noisy environment. Finally, several simulation experiments of the proposed model are conducted to find solutions of dynamic matrix inversion with different dimensions. Moreover, the realization of the tracking control of the robotic manipulator further illustrates the model’s superior convergence and robustness.

中文翻译：

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用于动态矩阵求逆的鲁棒预定义时间收敛归零神经网络


归零神经网络（ZNN）作为解决各种时变问题的经典而有效的方法，广泛应用于科学和工业领域。在对ZNN模型的大量研究中，其鲁棒性和收敛性一直是评价模型质量的两个重要标准。 ZNN模型的改进主要集中在其收敛速度上；然而，大多数先前的工作都忽略了其收敛速度的可调性，这限制了其在实际应用中的广泛推广。考虑到上述问题，设计了一个精心设计的激活函数（WDAF）。基于WDAF，提出了一种收敛速度可调的鲁棒预定义时间收敛ZNN（RPTCZNN）模型来解决动态矩阵求逆问题。此外，RPTCZNN模型收敛时间的上限在无噪声和噪声环境下通过严格的数学分析得到了理论上的验证。最后，对所提出的模型进行了多次仿真实验，以找到不同维度的动态矩阵求逆的解。此外，机器人机械臂跟踪控制的实现进一步说明了该模型优越的收敛性和鲁棒性。