A fixed-time converging neurodynamic approach with time-varying coefficients for l1-minimization problem

Abstract

In this paper, we propose a novel neurodynamic network to deal with l1-minimization problem. In the framework of the fixed-time converging neurodynamic network (FxNN), time-varying coefficients are introduced to design the time-varying fixed-time converging neurodynamic network (TFxNN). It is shown that the fixed-time stability of the proposed TFxNN via the Lyapunov stability conditions. It is further shown that the proposed TFxNN trajectories from any initial points quickly converge to the unique equilibrium solution in fixed-time. A distinctive feature of the proposed TFxNN is its flexibility to choose time-varying coefficients to accelerate convergence. Simulation results based on signal and image reconstruction are presented that the proposed neurodynamic network is feasible and effective.