Total variation of the control and energy of bilinear quantum systems

Nabile Boussaid (1) , Marco Caponigro (2) , Thomas Chambrion (3, 4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 M2N - Modélisation mathématique et numérique
3 CORIDA - Robust control of infinite dimensional systems and applications
4 IECL - Institut Élie Cartan de Lorraine

In the present note, we give two examples of bilinear quantum systems showing good agreement between the total variation of the control and the variation of the energy of solutions, with bounded or unbounded coupling term. The corresponding estimates in terms of the total variation of the control appear to be optimal.

Mots clés: Bilinear quantum systems; PDE; Control

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Total variation of the control and energy of bilinear quantum systems. Conference on Decision and Control, Dec 2013, Florence, Italy. pp.3714-3719. ⟨hal-00800548⟩