Robust zeroing neural networks with two novel power-versatile activation functions for solving dynamic Sylvester equation

In this work, two robust zeroing neural network (RZNN) models are presented for online fast solving of the dynamic Sylvester equation (DSE), by introducing two novel power-versatile activation functions (PVAF), respectively. Differing from most of the zeroing neural network (ZNN) models activated by recently reported activation functions (AF), both of the presented PVAF-based RZNN models can achieve predefined time convergence in noise and disturbance polluted environment. Compared with the exponential and finite-time convergent ZNN models, the most important improvement of the proposed RZNN models is their fixed-time convergence. Their effectiveness and stability are analyzed in theory and demonstrated through numerical and experimental examples.