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Controllability of the 1D Schrödinger equation using flatness

Philippe Martin 1 Lionel Rosier 2 Pierre Rouchon 1, 3
1 CAS - Centre Automatique et Systèmes
2 CAOR - Centre de Robotique
3 QUANTIC - QUANTum Information Circuits
MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - 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.
Keywords : Flatness Motion planning Schrödinger equation Partial differential equations Boundary control Exact controllability
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Submitted on : Friday, May 4, 2018 - 12:30:42 PM
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PARISTECH | ENSMP | TDS-MACS | ENS-PARIS | INSMI | INSTITUT-TELECOM | ENSMP_CAS | ENSMP_CAOR | INRIA | SORBONNE-UNIVERSITE | SU-SCIENCES | PSL | SU-TI

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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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