Constructive solution of a bilinear optimal control problem for a Schrödinger equation

Lucie Baudouin (1) , Julien Salomon (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient constructive method for solving a certain class of optimal control problems. This paper aims both at extending the results already available about these algorithms in the finite dimensional case (i.e., the time-discretized case) and at completing those of the continuous case. This paper starts with some results about the regularity of a functional related to a wide class of model in quantum chemistry. Those enable us to extend an inequality due to

Mots clés: Bilinear optimal control

Domaines: Equations aux dérivées partielles [math.AP]

Lucie Baudouin, Julien Salomon. Constructive solution of a bilinear optimal control problem for a Schrödinger equation. Systems and Control Letters, 2008, 57 (6), pp. 453-464; 150. ⟨hal-00271940⟩