Small time reachable set of bilinear quantum systems

Nabile Boussaid (1) , Marco Caponigro (2, 3) , Thomas Chambrion (4, 5)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 CCIB - Center for Computational and Integrative Biology [Camden]
3 Department of Mathematical Sciences [Camden]
4 CORIDA - Robust control of infinite dimensional systems and applications
5 IECN - Institut Élie Cartan de Nancy

This note presents an example of bilinear conservative system in an infinite dimensional Hilbert space for which approximate controllability in the Hilbert unit sphere holds for arbitrary small times. This situation is in contrast with the finite dimensional case and is due to the unboundedness of the drift operator.

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Small time reachable set of bilinear quantum systems. 51st Conference on Decision and Control (CDC), Dec 2012, Maui, HI, United States. pp.1083-1087, ⟨10.1109/CDC.2012.6426208⟩. ⟨hal-00710040⟩