Journal of Dynamical and Control Systems

, Volume 14, Issue 1, pp 43-70

First online:

Conic Distributions and Accessible Sets

  • B. LangerockAffiliated withDepartment of Architecture, St.-Lucas Institute for Higher Education in the Sciences & the Arts (W&K) Email author 

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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

2000 Mathematics Subject Classification

93Bxx 58E25