A Note on Controllability and non-Controllability for a Rayleigh Beam with Piezoelectric Actuator
Résumé
In this paper, the exact controllability problem for aRayleigh beam with piezoelectric actuator is considered.The main contributions of this work are to give the exactcontrollability results and to give the minimal controllabilitytime. Controllability results show that the space of control-lable initial data depends on the location of the actuator.The approach to prove controllability results is based onHilbert Uniqueness Method and some results on the theoryof Diophantine approximation. Due to the rotary inertiaterm in the Rayleigh beam equation, Rayleigh beam equa-tion possesses finite propagation speed, and consequently thecontrollability results hold when the control time surpassesa critical time. This critical time is proved to be the mini-mal controllability time by using the Riesz basis property ofexponential family inL2(0, T). The controllability in criticaltime is still an open problem.
Domaines
Systèmes et contrôle [cs.SY]
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