On the curves that may be approached by trajectories of a smooth control affine system

Jean-Baptiste Pomet 1, 2, 3
2 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
3 LJAD
JAD - Laboratoire Jean Alexandre Dieudonné
Abstract : In this paper, we give a characterization of the set of curves that may be approached by trajectories of a smooth control-ane nonlinear system, in the topology of uniform convergence. This characterization is in terms of the drift vector field and the distribution spanned by the Lie algebra generated by the control vector fields. The characterization is valid on open sets where this distribution has constant rank. These results also characterize the support of di↵usion processes with smooth coecients. ⇤
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Jean-Baptiste Pomet. On the curves that may be approached by trajectories of a smooth control affine system. Systems and Control Letters, Elsevier, 1999, 36 (2), pp.143 - 149. ⟨10.1016/S0167-6911(98)00086-3⟩. ⟨hal-01677090⟩

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