Journal of Dynamical and Control Systems

, Volume 14, Issue 1, pp 43–70

Conic Distributions and Accessible Sets


DOI: 10.1007/s10883-007-9034-4

Cite this article as:
Langerock, B. J Dyn Control Syst (2008) 14: 43. doi:10.1007/s10883-007-9034-4


Motivated by nonlinear control theory, we introduce the notion of conic distributions on a smooth manifold. We study topological and smoothness aspects of the set of accessible points associated with a conic distribution. We introduce the notion of abnormal paths and study their relation to boundary points of the accessible set. In particular, we provide sufficient conditions for the accessible set to be a maximal integral of the smallest integrable vector distribution containing the conic distribution. Under rather strong conditions, we are able to prove that the accessible set has the structure of a ‘manifold with corners’.

Key words and phrases

Geometric control theoryaccessible setsconic distributions

2000 Mathematics Subject Classification


Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of ArchitectureSt.-Lucas Institute for Higher Education in the Sciences & the Arts (W&K)GhentBelgium