Control of the bilinear Schrödinger equation for fully coupling potentials

Marco Caponigro (1, 2) , Ugo Boscain (3) , Thomas Chambrion (2, 1) , Mario Sigalotti (1, 2)

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

We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximations, lifted in SU(n). The method allows to estimate the L 1 norm of the control laws achieving controllability.

Mots clés: Control of the Schrödinger equation; Bilinear control systems on Lie groups; Quantum Control

Domaines: Optimisation et contrôle [math.OC]

Marco Caponigro, Ugo Boscain, Thomas Chambrion, Mario Sigalotti. Control of the bilinear Schrödinger equation for fully coupling potentials. 18th World Congress of the International Federation of Automatic Control (IFAC), 2011, Milan, Italy. ⟨hal-00589363⟩