Improved ZND model for solving dynamic linear complex matrix equation and its application

The online solving of a dynamic linear complex matrix equation (DLCME) is commonly encountered in many fields, and it exists for lots of engineering applications. For solving the DLCME, the gradient neural dynamics (GND) and the zeroing neural dynamics (ZND) are usually designed based on a predefined error function in scalar or matrix form to monitor the residual error convergence, respectively. In this paper, in order to improve the adaptability as the residual error decreasing with time and to release the limitation of convex activation function, an improved zeroing neural dynamics (IZND) model is proposed with a residual-based adaptive coefficient and a non-convex activation function. By using the Lyapunov stability theory, the global convergence and noise suppression of the proposed IZND model are theoretically discussed under the noise-free and noise-perturbed circumstances. Then, simulative verifications and a dynamic acoustic source localization application illustrate the efficacy and superiority of the proposed model for solving the DLCME. Comparing with some existing GND and ZND models, the proposed IZND model shows advanced performance in solution accuracy, noise suppression and convergence rate.