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Viability Kernels and Control Sets

Published online by Cambridge University Press:  15 August 2002

Dietmar Szolnoki
Dietmar Szolnoki*
Affiliation:
Universität Augsburg, Institut für Mathematik, Universitätsstraße 14, 86135 Augsburg, Germany; szolnoki@math.uni-augsburg.de.
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Abstract

This paper analyzes the relation of viability kernels and controlsets of control affine systems. A viability kernel describesthe largest closed viability domain contained in some closed subsetQ of the state space. On theother hand, control sets are maximal regions of the state spacewhere approximate controllability holds. It turns out thatthe viability kernel of Q can be represented by the union ofdomains of attraction of chain control sets, defined relativeto the given set Q.In particular, with thisresult control sets and their domains of attractioncan be computed using techniques for thecomputation of attractors and viability kernels.

Keywords

Control affine systemviability kernelreachable setcontrol setchain control setcontrol flow.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 175 - 185
Copyright
© EDP Sciences, SMAI, 2000

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