Saturated Boundary Feedback Stabilization for a Nonuniform Timoshenko Beam With Disturbances and Uncertainties

This article is concerned with the saturated feedback stabilization for a nonuniform Timoshenko beam with boundary control matched unknown internal uncertainties and external disturbances. An infinite-dimensional disturbance estimator without involving high gain is designed to estimate the total disturbances. By compensating/canceling the total disturbances in the feedback loop and combining with a collocated stabilizing controller without uncertainty, we propose an unsaturated feedback control to exponentially stabilize the system. Under the boundedness assumption on the magnitudes of the total disturbances, we further propose a saturated control to asymptotically stabilize the system. In addition to the actuator amplitude saturation, the control energy consumption is also reduced sharply. The well-posedness and stability of the closed-loop system are proved mainly by the semigroup theories and the frequency-domain method. Finally, some numerical simulations are carried out to validate the effectiveness of the proposed control strategy.