A Hybrid-Gain ZNN With Precisely Predefined-Time Convergence for Time-Variant LMVI and Its Applications to UR Robotic Arm and Multiagent System.

Abstract

Time-variant-gain zeroing neural networks (TVG-ZNNs) are among the most powerful solvers for time-variant linear matrix-vector inequalities (TVLMVIs). Although TVG-ZNNs with complex nonlinear activation functions achieve effective convergence within finite or predefined time, they incur high computational costs and face challenges in precisely predefining their actual convergence time. In contrast, TVG-ZNNs with linear activation functions offer lower computational costs but struggle to achieve convergence within a finite or predefined time. In addition, the gain values of most existing TVG-ZNNs tend to increase over time, resulting in a significant rise in computational costs. To address these contradictory issues, we propose a novel hybrid-gain ZNN without a nonlinear activation function (HG-ZNN-WNAF) to solve TVLMVIs in both noisy and noise-free environments. Specifically, a new hybrid gain is cleverly designed to construct the HG-ZNN-WNAF activated by a linear activation function, while ensuring that the gain value does not keep increasing over time. Unlike the state-of-the-art TVG-ZNNs with or without nonlinear activation functions, our proposed HG-ZNN-WNAF achieves precisely predefined-time convergence due to the hybrid gain, meaning its actual convergence time can be accurately predefined. Additionally, the piecewise design of the hybrid gain, along with the use of the simple linear activation function, effectively reduces the model's computational cost. Rigorous theoretical analysis demonstrates the precisely predefined-time convergence ability of the HG-ZNN-WNAF in both noisy and noise-free environments. Simulation and physical experiments validate the theoretical analysis and demonstrate that the HG-ZNN-WNAF achieves state-of-the-art performance in terms of convergence speed, robustness, and computational cost.