Parameter Estimation and Non-Collocated Adaptive Stabilization for a Wave Equation Subject to General Boundary Harmonic Disturbance

This paper is concerned with the parameter estimation and asymptotic stabilization of a 1-D wave equation that is subject to general harmonic disturbances at the controlled end and suffers from instability at the other end. First, we design an adaptive observer in terms of measured position and velocity. We then adopt the backstepping method for infinite-dimensional systems to design an observer-based output feedback law. The resulting closed-loop system is shown to be asymptotically stable. And the estimates of the parameters converge to the unknown parameters.