Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non-collocated control

摘要

This paper is concerned with the parameter estimation and stabilization of a one-dimensional wave equation with harmonic disturbance suffered by boundary observation at one end and the non-collocated control at the other end. An adaptive observer is designed in terms of measured velocity corrupted by harmonic disturbance with unknown magnitude. The backstepping method for infinite-dimensional system is adopted in the design of the feedback law. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity.