Adaptive stabilization of Kirchhoff's non-linear strings with output disturbances

Abstract

This paper is concerned with adaptive stabilization of an undamped non-linear string with disturbed outputs by boundary feedback control. The adaptive controller is constructed by the concept of high-gain adaptive feedback and the estimation mechanism for the unknown parameters of the measurement noise. The local existence and uniqueness of the solution of the closed-loop system are justified. Moreover, global existence and boundedness of the solution are shown for smooth and small initial data. The stability of the closed-loop system is proved such that the convergence of the system state to zero and the convergence of the estimated parameter to the unknown parameter are guaranteed for the smooth and small initial data.