2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58931Let $G$ 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.15 pagesOptimization and ControlMetric Geometry22E25; 93B03; 06F15; 49N35text