Prescribed time convergence and robust zeroing neural network for solving time-varying linear matrix equation

Zeroing neural network offers a new solution method to solve the time-varying linear matrix equation. As an important component, the activation function directly affects the performance of zeroing neural network in solving time-varying linear matrix equation. Focusing on the unification of prescribed time convergence and strong robustness without changing the basic structure of zeroing neural network, a novel activation function is proposed for the first time in this paper. Compared with commonly used activation functions in previous work, the novel activation function has superior performance for zeroing neural network to solve the time-varying linear matrix equation. The first item is global asymptotic convergence, capable of converging from random initial states to the theoretical solution. The second item is the prescribed time convergence, i.e. the upper bound of convergence time is only related to the parameters of the novel activation function and zeroing neural network, which facilitates the prediction of the convergence process. The third item is strong robustness, which ensures that the solution converges in various noisy environments. Theoretical analysis and comparative simulation experiments verify that zeroing neural network with the novel activation function has these performances for both low- or high-dimensional time-varying linear matrix equation.