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 publiéExternal document link
https://hal.archives-ouvertes.fr/hal-00866229Date
2015Journal name
European Journal of ControlVolume
22Published in
Paris
Pages
23-29
Publication identifier
Metadata
Show full item recordAbstract (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 controlRelated items
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