Noise-tolerant continuous-time Zhang neural networks for time-varying Sylvester tensor equations

Abstract

In this paper, to solve the time-varying Sylvester tensor equations (TVSTEs) with noise, we will design three noise-tolerant continuous-time Zhang neural networks (NTCTZNNs), termed NTCTZNN1, NTCTZNN2, NTCTZNN3, respectively. The most important characteristic of these neural networks is that they make full use of the time-derivative information of the TVSTEs’ coefficients. Theoretical analyses show that no matter how large the unknown noise is, the residual error generated by NTCTZNN2 converges globally to zero. Meanwhile, as long as the design parameter is large enough, the residual errors generated by NTCTZNN1 and NTCTZNN3 can be arbitrarily small. For comparison, the gradient-based neural network (GNN) is also presented and analyzed to solve TVSTEs. Numerical examples and results demonstrate the efficacy and superiority of the proposed neural networks.