Finite-time zeroing neural networks with novel activation function and variable parameter for solving time-varying Lyapunov tensor equation

Time-varying Lyapunov tensor equation (TV-LTE) is an extension of time-varying Lyapunov matrix equation (TV-LME), which represents more dimensions of data. In order to solve the TV-LTE more effectively, this paper proposes two improved zeroing neural network (ZNN) models based on a novel activation function and variable parameter, which have shorter convergence time and computation time. The novel activation function is composed of an exponential function and a sign-bi-power (SBP) function, which is mentioned as the exponential SBP (ESBP) function. Then, based on the ESBP activation function and the standard ZNN design method, an ESBP zeroing neural network (ES-ZNN) model is first provided. In addition, considering the relationship among the error matrix, design parameter and computational efficiency, this paper further designs an exponential parameter that varies dynamically with time and the error matrix. Replacing the fixed parameter with the proposed exponential variable parameter, an exponentially variable parameter ES-ZNN (EVPES-ZNN) model is provided to enhance the computational efficiency and convergence performance of the ES-ZNN model. Furthermore, the upper bounds on convergence time of such two ZNN models are theoretically calculated. Simulation experiments demonstrate the theoretical conclusion that the ES-ZNN and EVPES-ZNN models are able to solve the TV-LTE in finite-time.