Stabilization of one-dimensional wave equation with pointwise dissipation and external disturbance

In this paper, we are concerned with the stabilization of one-dimensional wave equation with pointwise dissipation and external disturbance. The active disturbance rejection control (ADRC) approach is adopted in investigation. By ADRC approach, an extended state observer (ESO) with time-varying high gain is designed to estimate the disturbance. The proposed control law cancels the disturbance by using the estimation. The closed-loop system is shown to be asymptotically stable. Finally, the simulation results are presented.