A Novel Robust and Predefined-Time Zeroing Neural Network Solver for Time-Varying Linear Matrix Equation

This paper develops a novel robust and predefined-time zeroing neural network (RPZNN) to solve the time-varying linear matrix equation (TVLME) in real time by developing an innovative activation function with a time parameter tf$$ {t}_f $$. Different from the existing ZNN solvers with complex convergence time bounds, the RPZNN solver obtains the real-time solution of the TVLME within an arbitrarily predefined time tf$$ {t}_f $$. Moreover, the RPZNN solver can freely adjust tf$$ {t}_f $$ to accommodate the requirements for various convergence rates, demonstrating its considerable flexibility. We conduct a theoretical analysis for the predefined-time convergence of the RPZNN solver and its robustness against additive noise interference. Furthermore, numerical experiments validate the effectiveness of the RPZNN in accurately addressing the TVLME and demonstrate its superior performance in terms of convergence rate and robustness when compared to several traditional or state-of-the-art ZNN solvers. Additionally, the RPZNN solver also exhibits excellent capabilities in dynamic alternating current (DAC) computing and the 6-link planar robot manipulator (6PRM) path-tracking task, highlighting its potential for wide-ranging applications.