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Controllability of the 1D Schrödinger equation using flatness

Philippe Martin 1 Lionel Rosier 2 Pierre Rouchon 1, 3
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
Abstract : We derive in a direct way the exact controllability of the 1D Schrödinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the derivatives of a “flat output”. This provides an explicit and very regular control achieving the exact controllability in the energy space.
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Philippe Martin, Lionel Rosier, Pierre Rouchon. Controllability of the 1D Schrödinger equation using flatness. Automatica, Elsevier, 2018, 91, pp.208 - 216. ⟨10.1016/j.automatica.2018.01.005⟩. ⟨hal-01769227⟩

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