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

In this paper, we propose a novel neurodynamic network to deal with l(1)-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.

Automated summary

In this paper, a novel neurodynamic network is proposed to solve the l(1)-minimization problem. The time-varying fixed-time converging neurodynamic network (TFxNN) is designed by introducing time-varying coefficients in the framework of the fixed-time converging neurodynamic network (FxNN). It is proven that the proposed TFxNN is fixed-time stable via Lyapunov stability conditions. Furthermore, it is shown that the proposed TFxNN quickly converges to the unique equilibrium solution from any initial points. An important feature of the proposed TFxNN is its flexibility to choose time-varying coefficients to accelerate convergence. Simulation results based on signal and image reconstruction validate the feasibility and effectiveness of the proposed neurodynamic network.