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

摘要

This paper considers the parameter estimation and stabilization of an unstable one-dimensional wave equation with matched general harmonic disturbance at the controlled end.The backstepping 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 goes to infinity.