A novel prescribed-time ZNN for solving time-varying complex Sylvester equation and application to pseudo-inverse

This paper innovatively designs a novel prescribed-time zeroing neural network (ZNN) model to solve the time-varying complex Sylvester (TVCS) equation, with its implementation embedded within the context of the pseudo-inverse of a matrix. By incorporating a trigonometric function term into the activation function, the proposed prescribed-time ZNN model is capable of achieving zero convergence within a predetermined time frame. The solution to the TVCS equation can be obtained within this prescribed time using our prescribed-time ZNN model. In addition, the robustness of our proposed the ZNN is shown by adding a large model-implementation error. Furthermore, a pseudo-inverse problem is utilized to demonstrate the efficacy of our proposed network model. Additionally, the paper provides insights into the parameter sensitivity and outlines strategies for parameter selection, both of which have been rigorously validated through numerical simulations.