Adaptive stabilization of a Kirchhoff’s non-linear beam with output disturbances

This paper is concerned with adaptive stabilization of an undamped non-linear beam 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 global existence and uniqueness of the solution of the closed-loop system is justified. 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.