Disturbance estimator based output feedback stabilizing control for an Euler-Bernoulli beam equation with boundary uncertainty

摘要

The disturbance estimator design proposed in [IEEE Trans. Automat. Control, 62(2017), 3774-3787.] is a systematic method to deal with the control-matched uncertainty. There are two main highlights for this approach: the disturbance estimator is not invoking high-gain and the derivative of disturbance is not required to be bounded. In this paper, we propose an output feedback control to stabilize an Euler-Bernoulli beam equation by following the idea of [IEEE Trans. Automat. Control, 62(2017), 3774-3787]. The main difficulty is that the boundary of the beam contains both interior uncertainty and the external disturbance. The well-posedness and the asymptotical stability of the closed-loop are proved by a novel transformation from which the nonlinear problem can be solved by method for linear ones.