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Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

Belhadj, Mohamed; Salomon, Julien; Turinici, Gabriel (2015), Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups, European Journal of Control, 22, p. 23-29. 10.1016/j.ejcon.2014.12.003

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-00866229
Date
2015
Journal name
European Journal of Control
Volume
22
Published in
Paris
Pages
23-29
Publication identifier
10.1016/j.ejcon.2014.12.003
Metadata
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Author(s)
Belhadj, Mohamed
Salomon, Julien
Turinici, Gabriel cc
Abstract (EN)
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 where an infinite number of perturbations occurs. In addition, the techniques invoked in the proof allow us to obtain generic necessary and sufficient conditions for ensemble controllability.
Subjects / Keywords
perturbations; Lie group controllability; bilinear syst em; quantum control

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