Solving Time-Varying Complex-Valued Sylvester Equation via Adaptive Coefficient and Non-Convex Projection Zeroing Neural Network

The time-varying complex-valued Sylvester equation (TVCVSE) often appears in many fields such as control and communication engineering. Classical recurrent neural network (RNN) models (e.g., gradient neural network (GNN) and zeroing neural network (ZNN)) are often used to solve such problems. This paper proposes an adaptive coefficient and non-convex projection zeroing neural network (ACNPZNN) model for solving TVCVSE. To enhance its adaptability as residual error decreasing as time, an adaptive coefficient is designed based on residual error. Meanwhile, this paper breaks the convex constraint by constructing two complex-valued non-convex projection activation functions from two different aspects. Moreover, the global convergence of the proposed model is proved, the anti-noise performance of the ACNPZNN model under different noises is theoretically analyzed. Finally, simulation experiments are provided to compare the convergence performance of different models, which simultaneously verifies the effectiveness and superiority of the proposed model.