Adaptive error feedback regulation problem for an euler-bernoulli beam equation with general unmatched boundary harmonic disturbance

This paper is concerned with the adaptive error feedback regulator problem whereby the 1D Euler-Bernoulli beam equation with general unknown amplitude harmonic disturbance is rejected and general harmonic reference signal is tracked. We first construct one auxiliary system in which the measured error becomes the boundary output. Then an adaptive observer is designed in terms of the measured error (its time derivative) to recover the state of the auxiliary system and estimate the unknown parameters. Last, we construct another auxiliary system in which the control and the unmatched disturbance become matched and thus obtain the controller which regulates the error output to zero and keeps the states bounded.