A predefined-time and anti-noise varying-parameter ZNN model for solving time-varying complex Stein equations

A predefined-time and anti-noise varying-parameter zeroing neural network (PTAN-VPZNN) is designed to resolve time-varying complex Stein equations in this paper. Differing from the existing ZNNs, the merits of the proposed PTAN-VPZNN include: 1) a varying parameter that improves ZNN model’s convergence speed, which is more compatible with characteristics of the actual hardware parameter; 2) a noise-tolerant activation function which enables the PTAN-VPZNN model to solve Stein equations under noisy environments. Thence, the PTAN-VPZNN model has better convergence performance and noise immunity ability. Moreover, the predefined-time convergence of the PTAN-VPZNN is presented and the robustness of the PTAN-VPZNN is analyzed under constant noise, through rigorous theoretical derivations. Numerical studies demonstrate that the performance of the PTAN-VPZNN is better than the existing ZNNs including a linear ZNN (LZNN), a nonlinear ZNN (NLZNN), a finite-time convergent ZNN (FTCZNN) and a predefined-time convergent ZNN (PTCZNN), when solving Stein equations with or without noise involved. Finally, the PTAN-VPZNN is applied to a mobile manipulator for completing a path-tracking task, showing its potential application in robot control.