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Output Feedback Stabilization for One-Dimensional Wave Equation Subject to Boundary Disturbance

We consider boundary output feedback stabilization for a one-dimensional anti-stable wave equation subject to general control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted in investigation. Using the output of the system, we first design a variable structure unknown input type state observer which is shown to be exponentially convergent. The disturbance is estimated, in real time, through an extended state observer for an ODE reduced from the PDE observer. The disturbance is then canceled in the feedback loop by its approximated value. The stability of the resulting closed-loop system is proven. Simulation results are presented to validate the theoretical conclusions and to exhibit the peaking value reduction by time varying gain instead of constant high gain.