A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function

Nonlinear activation functions play an important role in zeroing neural network (ZNN), and it has be proved that ZNN can achieve finite-time convergence when the sign-bi-power (SBP) activation function is explored. However, its upper bound depends on initial states of ZNN seriously, which will restrict some practical applications since the knowledge of initial conditions is generally unavailable in advance. Besides, SBP activation function does not make ZNN reject external disturbances simultaneously. To address the above two issues encountered by ZNN, by suggesting a new nonlinear activation function, a robust and fixed-time zeroing neural dynamics (RaFT-ZND) model is proposed and analyzed for time-variant nonlinear equation (TVNE). As compared to the previous ZNN model with SBP activation function, the RaFT-ZND model not only converges to the theoretical solution of TVNE within a fixed time, but also rejects external disturbances to show good robustness. In addition, the upper bound of the fixed-time convergence is theoretically computed in mathematics, which is independent of initial states of the RaFT-ZND model. At last, computer simulations are conducted under external disturbances, and comparative results demonstrate the effectiveness, robustness, and advantage of the RaFT-ZND model for solving TVNE. (C) 2019 Elsevier B.V. All rights reserved.