Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point
2016 (English)In: Nonlinear Analysis. Hybrid Systems., ISSN 1751-570X, E-ISSN 1878-7460, Vol. 20, 1-20 p.Article in journal (Refereed) Published
Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution. ©2015 The Authors. Published by Elsevier Ltd.
Place, publisher, year, edition, pages
London: Elsevier, 2016. Vol. 20, 1-20 p.
hybrid automata, hybrid systems, validated numerics, simulation, model validation, reliability
IdentifiersURN: urn:nbn:se:hh:diva-29869DOI: 10.1016/j.nahs.2015.10.004ISI: 000370898700001ScopusID: 2-s2.0-84947996983OAI: oai:DiVA.org:hh-29869DiVA: diva2:876228
FunderKnowledge Foundation, 20100314
A preliminary version of this paper was published in the proceedings of CPSNA 2013. This work was supported by the US National Science Foundation, awards NSF-CPS-1136099/1136104, the Swedish Knowledge Foundation (KK) and the Center for Research on Embedded Systems (CERES) grant number 20100314, and EPSRC grant number EP/C01037X/1.2015-12-022015-12-022016-03-23Bibliographically approved