Output Feedback Stabilization for a 1-D Conservative Wave Equation with General Corrupted Boundary Observation

In this paper, we consider the output feedback stabilization of a 1-D conservative wave equation, where the boundary velocity observation is subjected to a general disturbance. We first consider using only the output of the system to online estimate the disturbance by active disturbance rejection control (ADRC). The observer is designed in terms of the disturbance estimator. Then we present an observer-based output feedback law to achieve stabilization. The estimated disturbance is proved to be convergent to the unknown disturbance and the velocity signal can be asymptotically recovered when time tends to infinity. At the same time, the asymptotic stability of the closed-loop system can be verified. Finally, some simulations are given to illustrate the theoretical conclusions.