Boundary output feedback stabilization for a cascaded wave PDE-ODE system with velocity recirculation and matched disturbance

In this paper, we are concerned with a boundary stabilization problem of a cascaded wave PDE-ODE (partial differential equation-ordinary differential equation) system with velocity recirculation and matched disturbance. First, an auxiliary PDE system is proposed to estimate the boundary disturbance by active disturbance rejection control (ADRC) method. Next with the estimation of the disturbance in hand, a state observer is constructed to recover the state of the PDE-ODE system. Then we design an output feedback controller under which the solution of the resulting closed-loop system is bounded and the state of the cascaded wave PDE-ODE system decays exponentially. Finally, some simulation examples are given to illustrate the effectiveness of the designed controller.