Controllability of the 1D Schrödinger equation using flatness

Philippe Martin; Lionel Rosier; Pierre Rouchon

doi:10.1016/j.automatica.2018.01.005

Journal articles

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

ENS-PSL - 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.

Keywords : Schrödinger equation Partial differential equations Boundary control Exact controllability Motion planning Flatness

Document type :

Journal articles

Domain :

Mathematics [math] / Optimization and Control [math.OC]

Engineering Sciences [physics] / Automatic

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Submitted on : Friday, May 4, 2018 - 12:30:42 PM
Last modification on : Wednesday, June 8, 2022 - 12:50:07 PM
Long-term archiving on: : Monday, September 24, 2018 - 4:16:02 PM

Controllability of the 1D Schrödinger equation using flatness

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