Output Tracking of an Anti-Stable Wave Equation Subject to Boundary Disturbance with Non-Collocated Feedback

In this paper, we study the output tracking problem of an anti-stable wave equation subject to boundary control matched disturbance. The desired reference tracking is derived by using the differential flatness method, which allows us to realize the tracking of suitably prescribed trajectories for the system output. To stabilize the tracking error system, a feedback control is designed, which contains a non-collocated part and an estimation of disturbance based on the active disturbance rejection control (ADRC) approach. The closed-loop tracking error system is proved to be asymptotically stable and the tracking performance is illustrated by numerical simulation.