Identification and stabilization for a one-dimensional wave equation with boundary output unknown constant and non-collocated control

We are concerned with parameter estimation and stabilization of a one-dimensional wave equation with unknown constant signal disturbance suffered from boundary observation at one end and the non-collocated control at another end. An adaptive observer is designed in terms of measured velocity with unknown constant disturbance. The backstepping method is adopted in design of the feedback law. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the unknown constant is estimated.