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Viability Kernels and Exit Tubes

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Book cover Viability Theory

Part of the book series: Systems & Control: Foundations & Applications ((MBC))

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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.

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Authors and Affiliations

  1. EDOMADE (Ecole Doctorale de Mathématique de la Décision), Université de Paris-Dauphine, F-75775, Paris cedex 16, France

    Jean-Pierre Aubin

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  1. Jean-Pierre Aubin
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Aubin, JP. (2009). Viability Kernels and Exit Tubes. In: Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4910-4_6

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