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Viability Kernels and Exit Tubes

  • Jean-Pierre Aubin
Part of the Systems & Control: Foundations & Applications book series (MBC)

Abstract

If a closed subset K is not a viability domain, the question arises as to whether there are closed viability subsets of K viable under F and even, whether there exists a largest closed subset of K viable under F. The answer is positive for Marchaud maps, and we call viability kernel of a closed subset K the largest closed subset viable under F contained in K. Actually, we shall prove in the first section that it is equal to the set of initial states of K from which there exists at least one solution viable in K.

Keywords

Closed Subset Differential Inclusion Exit Time Nonempty Interior Nonempty Open Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2009

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.EDOMADE (Ecole Doctorale de Mathématique de la Décision)Université de Paris-DauphineParis cedex 16France

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