Stabilization and parameter estimation for an Euler-Bernoulli beam equation with uncertain harmonic disturbance under boundary output feedback control

This paper is concerned with the boundary stabilization and parameter estimation of an Euler-Bernoulli beam equation with one end fixed, and control and uncertain amplitude of harmonic disturbance at another end. A high-gain adaptive regulator is designed in terms of measured collocated end velocity. The existence and uniqueness of the classical solution as well as smooth solution of the closed-loop system are justified. It is shown that the state of the system approaches the standstill as time goes to infinity and meanwhile the estimated parameter converges to the unknown parameter.