Stabilization and regulator design for a one‐dimensional unstable wave equation with input harmonic disturbance

Abstract

SUMMARY This paper considers the parameter estimation and stabilization of a one‐dimensional wave equation with instability suffered at one end and uncertainty of 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. Copyright © 2011 John Wiley & Sons, Ltd.