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.

Robust Finite-Time Zeroing Neural Networks With Fixed and Varying Parameters for Solving Dynamic Generalized Lyapunov Equation.

For solving dynamic generalized Lyapunov equation, two robust finite-time zeroing neural network (RFTZNN) models with stationary and nonstationary parameters are generated through the usage of an improved sign-bi-power (SBP) activation function (AF). Taking differential errors and model implementation errors into account, two corresponding perturbed RFTZNN models are derived to facilitate the analyses of robustness on the two RFTZNN models. Theoretical analysis gives the quantitatively estimated upper bounds for the convergence time (UBs-CT) of the two derived models, implying a superiority of the convergence that varying parameter RFTZNN (VP-RFTZNN) possesses over the fixed parameter RFTZNN (FP-RFTZNN). When the coefficient matrices and perturbation matrices are uniformly bounded, residual error of FP-RFTZNN is bounded, whereas that of VP-RFTZNN monotonically decreases at a super-exponential rate after a finite time, and eventually converges to 0. When these matrices are bounded but not uniform, residual error of FP-RFTZNN is no longer bounded, but that of VP-RFTZNN still converges. These superiorities of VP-RFTZNN are illustrated by abundant comparative experiments, and its application value is further proved by an application to robot.