Bilinear control of high frequencies for a 1D Schrödinger equation

Abstract : In this article, we consider a 1D linear Schrödinger equation with potential V and bilinear control. Under appropriate assumptions on V , we prove the exact controllability of high frequencies, in H 3 , locally around any H 3-trajectory of the free system. In particular, any initial state in H 3 can be steered to a regular state, for instance a nite sum of eigen-functions of (−∆ + V). This fact, coupled with a previous result due to Nersesyan, proves the global exact controllability of the system in H 3 , with smooth controls, under appropriate assumptions.
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Karine Beauchard, Camille Laurent. Bilinear control of high frequencies for a 1D Schrödinger equation. Mathematics of Control, Signals, and Systems, Springer Verlag, 2017, 29 (2), pp.article 11. ⟨10.1007/s00498-017-0187-8⟩. ⟨hal-01333625⟩

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