P. Nistri & M. Quincampoix


Titre: "On open-loop and feedback attainability of a closed set for nonlinear control systems."


Résumé: In this Note, we investigate the existence of controls which allow to reach a given closed set $K$ through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach $K$. When $K$ is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not $C^1$, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set $K$ in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.










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