Backstepping Approach to the Adaptive Regulator Design for a One-Dimensional Wave Equation with General Input Harmonic Disturbance

This paper considers the parameter estimation and stabilization of an unstable one-dimen- sional wave equation with matched general harmonic disturbance at the controlled end. The back- stepping method for infinite-dimensional system is adopted in the design of the adaptive regulator. 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 unes tn ~n~nitv