Output Feedback Stabilization for Multi-Dimensional Wave Equation with Boundary Control Matched Disturbance

In this paper, we consider boundary output feedback stabilization for a multidimensional wave equation with boundary control matched unknown nonlinear internal uncertainty and external disturbance. A new unknown input type extended state observer is proposed to recover both state and total disturbance which consists of internal uncertainty and external disturbance by using the hidden regularity of the wave equation. By the active disturbance rejection control (ADRC) strategy, the total disturbance is compensated (canceled) in the feedback loop, which together with a collocated stabilizing controller without uncertainty, leads to an output feedback stabilizing feedback control. It is shown that the resulting closed-loop system is well-posed and asymptotically stable under weak assumption on internal uncertainty and external disturbance. The numerical experiments are carried out to show the effectiveness of the proposed scheme.