Accelerating noise-tolerant zeroing neural network with fixed-time convergence to solve the time-varying Sylvester equation

Abstract

Recently, Xiao et al. presented a new noise-tolerant zeroing neural network (NNTZNN) model that can achieve fixed-time convergence even in the presence of some noise to solve the time-varying Sylvester equation. In this brief paper, we extend it to more general case through introducing a power parameter k while retaining its fixed-time convergence and noise-tolerant performance. The new proposed model is here named as the accelerating noise-tolerant zeroing neural network (ANTZNN) model since its fixed convergence time can be shorter than that of the NNTZNN model in certain model parameter ranges. These parameter ranges and the convergence of the ANTZNN model are theoretically analyzed in detail. Numerical experiments are performed to confirm the theoretical results, including the numerical comparisons with the known NNTZNN model under different parameter settings. Furthermore, the ANTZNN model is also applied to the control of robot manipulator, thus showing the applicability of the proposed ANTZNN model.