Viability Kernels and Control Sets

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

Received: 10 December 1998
Revised: 14 December 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.