Exact controllability for a Rayleigh beam with piezoelectric actuator
Abstract
In this paper, exact controllability for a Rayleigh beam with piezoelectric actuator is considered. Controllability results show that the space of controllable initial data depends on the regularity of the control function and the location of the actuator. Two different spaces of control function, $L^2(0,T)$ and $(H^1(0,T))'$, correspond to two different controllability, $L^2$-controllability and $(H^1)'$-controllability. The approach to prove controllability results is based on Hilbert Uniqueness Method. Some non-controllability results are also obtained. In particular, non-controllability in short control time is studied by using Riesz basis property of exponential family in $L^2(0,T)$. Due to this non-controllability result, minimal time for the exact controllability is obtained.
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