A noise-tolerant zeroing neural network with fixed-time convergence for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors

Multi-linear systems play a crucial role in various practical applications such as high-dimensional partial differential equations (PDEs), signal processing, and high-order statistics. In this paper, we propose a noise-tolerant zeroing neural network (NTZNN) model with fixed-time convergence activated by a new nonlinear activation function for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors. The detailed theoretical analysis demonstrates that the NTZNN model is stable in the sense of Lyapunov stability theory and achieves fixed-time convergence with or without the presence of noises. Furthermore, compared with existing neural network models, the proposed NTZNN model significantly improves the convergence rate while maintaining noise tolerance. Numerical experiments further show the effectiveness and superiority of the proposed NTZNN model.