Controllability properties of discrete-spectrum Schrödinger equations

Thomas Chambrion (1, 2) , Paolo Mason (1, 2) , Mario Sigalotti (1, 2) , Ugo Boscain (3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We state an approximate controllability result for the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. This result applies both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. In addition we get some controllability properties for the density matrix. Finally we show, by means of specific examples, how these results can be applied.

Domaines: Optimisation et contrôle [math.OC]

Thomas Chambrion, Paolo Mason, Mario Sigalotti, Ugo Boscain. Controllability properties of discrete-spectrum Schrödinger equations. Conference on Decision and Control, Dec 2008, Cancun, Mexico. pp.4540, ⟨10.1109/CDC.2008.4738720⟩. ⟨hal-00589550⟩