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.
Sommaire