Periodic control laws for bilinear quantum systems with discrete spectrum

Nabile Boussaid (1) , Marco Caponigro (2, 3) , Thomas Chambrion (2, 3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy

We provide bounds on the error between dynamics of an infinite dimensional bilinear Schrodinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations to obtain constructive controllability results. As an illustration, the methods are applied on a model of a 2D rotating molecule.

Keywords: Bilinear Schrodinger equation; weakly-coupled systems; Galerkin approximations

Domains: Optimization and Control [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Periodic control laws for bilinear quantum systems with discrete spectrum. American Control Conference 2012, Jun 2012, Montreal, Canada. pp.5619-5824. ⟨hal-00637116⟩