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Attainable sets for left invariant control systems and Carnot-Caratheodory metrics on nilpotent Lie groups

V. M. Gichev
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Abstract

Let $G$ be a semidirect product of a simply connected nilpotent Lie group and $\R$. For a left invariant control system on $G$ with a convex cone as a control domain, it is proved that the attainable sets coincides with a "halfspace" if the degree of contact of the with some special subspaces is sufficiently high.

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V. M. Gichev. 2000-03-29. Attainable sets for left invariant control systems and Carnot-Caratheodory metrics on nilpotent Lie groups. https://arxiv.org/abs/math/0003203

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