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

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

2000-03-29

arxiv.org/abs/math/0003203v1

Proceedings of Conference "Analysis and Geometry" in honour of the 70th birthday of Professor Yu. G. Reshetnyak, Novosibirsk,

Mathematics

Optimization and Control

15 pages

Scientific paper

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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