Simultaneous controllability and discrimination of collections of perturbed bilinear control systems on the Lie group SU(N)

Mohamed Belhadj (1) , Julien Salomon (2) , Gabriel Turinici (2)

1 Département de Mathématiques, Institut Supérieur des Mathématiques Appliquées et d'Informatique de Kairouan
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The controllability of bilinear systems is well understood for finite dimensional isolated systems where the control can be implemented exactly. However when perturbations are present some interesting theoretical questions are raised. We consider in this paper a control system whose control cannot be implemented exactly but is shifted by a time independent constant in a discrete list of possibilities. We prove under general hypothesis that the collection of possible systems (one for each possible perturbation) is simultaneously controllable with a common control. The result is extended to the situations where the perturbations are constant over a common, long enough, time frame. We apply the result to the controllability of quantum systems. Furthermore, some examples and a convergence result are presented for the situation when an infinite number of perturbations occur.

Domaines: Optimisation et contrôle [math.OC]

Mohamed Belhadj, Julien Salomon, Gabriel Turinici. Simultaneous controllability and discrimination of collections of perturbed bilinear control systems on the Lie group SU(N). 2014. ⟨hal-00866229v3⟩