Conic Distributions and Accessible Sets Article

First Online: 25 January 2008 Received: 06 December 2006 Revised: 06 March 2007 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
Abstract 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 theory accessible sets conic distributions

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Authors and Affiliations 1. Department of Architecture St.-Lucas Institute for Higher Education in the Sciences & the Arts (W&K) Ghent Belgium