Reachability in one-dimensional controlled polynomial dynamical systems

Authors:
Margarita Korovina;Nicolai Vorobjov
Affiliations:
The University of Manchester, UK,IIS, SB RAS, Novosibirsk, Russia;University of Bath, UK
Venue:
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
Year:
2011

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Information and Computation

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Abstract

In this paper we investigate a case of the reachability problem in controlled o-minimal dynamical systems. This problem can be formulated as follows. Given a controlled o-minimal dynamical system initial and target sets, find a finite choice of time points and control parameters applied at these points such that the target set is reachable from the initial set. We prove that the existence of a finite control strategy is decidable and construct a polynomial complexity algorithm which generates finite control strategies for one-dimensional controlled polynomial dynamical systems. For this algorithm we also show an upper bound on the numbers of switches in finite control strategies.