Predefined-Time Zeroing Neural Networks With Independent Prior Parameter for Solving Time-Varying Plural Lyapunov Tensor Equation.

Abstract

As an extension of the Lyapunov equation, the time-varying plural Lyapunov tensor equation (TV-PLTE) can carry multidimensional data, which can be solved by zeroing neural network (ZNN) models effectively. However, existing ZNN models only focus on time-varying equations in field of real number. Besides, the upper bound of the settling time depends on the value of ZNN model parameters, which is a conservative estimation for existing ZNN models. Therefore, this article proposes a novel design formula for converting the upper bound of the settling time into an independent and directly modifiable prior parameter. On this basis, we design two new ZNN models called strong predefined-time convergence ZNN (SPTC-ZNN) and fast predefined (FP)-time convergence ZNN (FPTC-ZNN) models. The SPTC-ZNN model has a nonconservative upper bound of the settling time, and the FPTC-ZNN model has excellent convergence performance. The upper bound of the settling time and robustness of the SPTC-ZNN and FPTC-ZNN models are verified by theoretical analyses. Then, the effect of noise on the upper bound of settling time is discussed. The simulation results show that the SPTC-ZNN and FPTC-ZNN models have better comprehensive performance than existing ZNN models.