Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation

The zeroing neural network (ZNN) activated by nonlinear activation functions plays an important role in many fields. However, conventional ZNN can only realize finite-time convergence, which greatly limits the application of ZNN in a noisy environment. Generally, finite-time convergence depends on the original state of ZNN, but the original state is often unknown in advance. In addition, when meeting with different noises, the applied nonlinear activation functions cannot tolerate external disturbances. In this article, on the strength of this idea, two prescribed-time and robust ZNN (PTR-ZNN) models activated by two nonlinear activation functions are put forward to address the time-variant Stein matrix equation. The proposed two PTR-ZNN models own two remarkable advantages simultaneously: 1) prescribed-time convergence that does not rely on original states and 2) superior noise-tolerance performance that can tolerate time-variant bounded vanishing and nonvanishing noises. Furthermore, the detailed theoretical analysis is provided to guarantee the prescribed-time convergence and noise-tolerance performance, with the convergence upper bounds of steady-state residual errors calculated. Finally, simulative comparison results indicate the effectiveness and the superiority of the proposed two PTR-ZNN models for the time-variant Stein matrix equation solving.