A Robust Predefined-Time Convergence Zeroing Neural Network for Dynamic Matrix Inversion

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.

Automated summary

The zeroing neural network (ZNN) is a classical and effective method for solving various time-varying problems, widely applied in scientific and industrial realms. Robustness and convergence are two essential criteria in evaluating the quality of the ZNN model, but the adjustability of its convergence speed has been neglected in prior works. To address this issue, a well-designed activation function (WDAF) is proposed, leading to the development of a robust predefined-time convergence ZNN (RPTCZNN) model with adjustable convergence speed. The model is validated through mathematical analysis and simulation experiments, showcasing its superior convergence and robustness in solving dynamic matrix inversion problems and enabling tracking control of robotic manipulators.