Adaptive Output Feedback Stabilization for One-Dimensional Wave Equation with Corrupted Observation by Harmonic Disturbance

Abstract

In this paper, we are concerned with the output feedback stabilization of a one-dimensional wave equation with an unstable term at one end, and the observation suffered by a general harmonic disturbance with unknown magnitudes at the other end. An adaptive observer is designed in terms of the corrupted observation. The backstepping method for infinite-dimensional systems is adopted in the design of the feedback law. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameters are shown to be convergent to the unknown parameters as time goes to infinity.