Jin Jie, Zhu Jingcan, Zhao Lv, Chen Lei, Chen Long, Gong Jianqiang
IEEE Trans Cybern. 2023 Jun;53(6):3887-3900. doi: 10.1109/TCYB.2022.3179312. Epub 2023 May 17.
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.
作为解决各种时变问题的经典且有效方法，归零神经网络（ZNN）在科学和工业领域得到了广泛应用。在对ZNN模型的大量研究中，其鲁棒性和收敛性一直是评估模型质量的两个重要标准。ZNN模型的改进主要集中在收敛速度上；然而，在大多数先前的工作中，其收敛速度的可调节性被忽视了，这限制了它在实际应用中的广泛推广。考虑到上述问题，设计了一种精心设计的激活函数（WDAF）。基于WDAF，提出了一种具有可调收敛速度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，通过在无噪声和有噪声环境下的严格数学分析，从理论上验证了RPTCZNN模型收敛时间的上界。最后，对所提出的模型进行了若干仿真实验，以求解不同维度的动态矩阵求逆问题。此外，机器人机械手跟踪控制的实现进一步说明了该模型具有卓越的收敛性和鲁棒性。
