A Predefined-Time Adaptive Zeroing Neural Network for Solving Time-Varying Linear Equations and Its Application to UR 5 Robot.

Time-varying linear equations (TVLEs) play a fundamental role in the engineering field and are of great practical value. Existing methods for the TVLE still have issues with long computation time and insufficient noise resistance. Zeroing neural network (ZNN) with parallel distribution and interference tolerance traits can mitigate these deficiencies and thus are good candidates for the TVLE. Therefore, a new predefined-time adaptive ZNN (PTAZNN) model is proposed for addressing the TVLE in this article. Unlike previous ZNN models with time-varying parameters, the PTAZNN model adopts a novel error-based adaptive parameter, which makes the convergence process more rapid and avoids unnecessary waste of computational resources caused by large parameters. Moreover, the stability, convergence, and robustness of the PTAZNN model are rigorously analyzed. Two numerical examples reflect that the PTAZNN model possesses shorter convergence time and better robustness compared with several variable-parameter ZNN models. In addition, the PTAZNN model is applied to solve the inverse kinematic solution of UR 5 robot on the simulation platform CoppeliaSim, and the results further indicate the feasibility of this model intuitively.