Exact controllability in projections of the bilinear Schrödinger equation

Marco Caponigro (1) , Mario Sigalotti (2, 3)

1 M2N - Modélisation mathématique et numérique
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 GECO - Geometric Control Design

We consider the bilinear Schrödinger equation with discrete-spectrum drift. We show, for n ∈ N arbitrary, exact controllability in projections on the first n given eigenstates. The controllability result relies on a generic controllability hypothesis on some associated finite-dimensional approximations. The method is based on Lie-algebraic control techniques applied to the finite-dimensional approximations coupled with classical topological arguments issuing from degree theory.

Domaines: Optimisation et contrôle [math.OC]

Marco Caponigro, Mario Sigalotti. Exact controllability in projections of the bilinear Schrödinger equation. 2017. ⟨hal-01509971v2⟩