Output feedback stabilization for a wave-ODE cascaded system subject to uncertain disturbance

In this paper, we consider output feedback stabilization for a wave-ODE cascaded system with uncertain disturbance flowing the control end. Firstly, a disturbance estimator is designed by the new active disturbance rejection control (ADRC) approach that we propose two auxiliary systems. Then, we design an observer for the coupled system based on the idea that copy of the original system plus injection of the output estimation error. Finally, by the backstepping method, we design an output feedback control and obtain the exponential stabilization of the closed-loop system, which consists of the original coupled system, the observer, two new auxiliary systems, and the control. Due to the existence of the in-domain anti-damping in wave equation, the proposed two auxiliary systems are different from those in the previous literature. And their designs are inspired by the design idea of the observer. Some numerical simulations are given to illustrate the effectiveness of the control.