Control systems of zero curvature are not necessarily trivializable

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dc.creatorSerres, Ulysse
dc.date2009-02-13
dc.date.accessioned2026-07-07T12:41:37Z
dc.date.available2026-07-07T12:41:37Z
dc.descriptionA control system $\dot{q} = f(q,u)$ is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form $\dot{q} = f(u)$. In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, $f$ and $\partial f/\partial u$ commute. Characterizations are given in terms of feedback invariants of the system (its control curvature and its centro-affine curvature) and thus are completely intrinsic. To conclude we apply the obtained results to Zermelo-like problems on Riemannian manifolds.
dc.identifierhttps://arxiv.org/abs/0902.2332
dc.identifierhttp://arxiv.org/abs/0902.2332
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219833
dc.subjectOptimization and Control
dc.subjectDifferential Geometry
dc.subject34K35; 37C10; 37E35; 53B99; 93C10; 93C15
dc.titleControl systems of zero curvature are not necessarily trivializable
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