Residual Error Feedback Zeroing Neural Network for Solving Time-Varying Sylvester Equation

In many fields, the issue of solving the time-varying Sylvester equation (TVSE) is commonly encountered. Consequently, finding its exact solution has become a research hotspot. In general, the ZNN and IEZNN models are the most useful algorithms that are frequently utilized to solve the TVSE problem. However, the ZNN model is borned with noise susceptibility and the IEZNN model loses the adaptive performance due to its constant coefficient in solving the TVSE problem. In this paper, a residual error feedback zeroing neural network (REFZNN) is proposed to adaptively solve the TVSE problem. The REFZNN model feeds back the residual error to the solustion system, which forms a feedback regulation to reduce the residual error between the system output and the system target. Then, the convergence and noise patience of the REFZNN model are proved by theoretical analyses. Finally, the validity of the proposed model is verified by designing computer simulation experiments and its superiority is confirmed by the performance comparisons with the ZNN and IEZNN models.