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Issue		ESAIM: COCV Volume 5, 2000
Page(s)		175 - 185
DOI		10.1051/cocv:2000106

DOI: 10.1051/cocv:2000106

ESAIM: COCV, March 2000, Vol. 5, p. 175-185

Viability kernels and control sets

Dietmar Szolnoki
Universität Augsburg, Institut für Mathematik, Universitätsstraße 14, 86135 Augsburg, Germany; (szolnoki@math.uni-augsburg.de)

Received December 10, 1998. Revised December 14, 1999.

Abstract: This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular, with this result control sets and their domains of attraction can be computed using techniques for the computation of attractors and viability kernels.

Keywords and phrases: Control affine system, viability kernel, reachable set, control set, chain control set, control flow.

AMS Subject Classification: 34H05, 93B03

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