Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore-Penrose Inverse.

This article proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute the time-varying tensor Moore-Penrose (MP) inverse. The PTANN model incorporates a novel adaptive parameter and activation function, enabling it to achieve strongly predefined-time convergence. Unlike traditional time-varying parameters that increase over time, the adaptive parameter is proportional to the error norm, thereby better allocating computational resources and improving efficiency. To further enhance efficiency, the ET-PTANN model combines an event trigger with the evolution formula, resulting in the adjustment of step size and reduction of computation frequency compared to the PTANN model. By conducting mathematical derivations, the article derives the upper bound of convergence time for the proposed neural network models and determines the minimum execution interval for the event trigger. A simulation example demonstrates that the PTANN and ET-PTANN models outperform other related neural network models in terms of computational efficiency and convergence rate. Finally, the practicality of the PTANN and ET-PTANN models is demonstrated through their application for mobile sound source localization.

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

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.