Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Konečný, Michal, Taha, Walid, Bartha, Ferenc A., Duracz, Jan, Duracz, Adam and Ames, Aaron D. (2016). Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point. Nonlinear Analysis : Hybrid Systems, 20 , pp. 1-20.

Abstract

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.

Publication DOI: https://doi.org/10.1016/j.nahs.2015.10.004
Divisions: Engineering & Applied Sciences > Computer science research group
Engineering & Applied Sciences > Computer science
Additional Information: © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Funding: US National Science Foundation (awards NSF-CPS-1136099/1136104); Swedish Knowledge Foundation (KK) and the Center for Researchon Embedded Systems (CERES) (grant 20100314); and EPSRC (grant EP/C01037X/1).
Uncontrolled Keywords: hybrid automata,hybrid systems,rigorous computations,validated numerics,Zeno behavior,Control and Systems Engineering,Computer Science Applications,Analysis
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://www.sci ... 0606?via%3Dihub (Publisher URL)
Published Date: 2016-05
Authors: Konečný, Michal ( 0000-0003-2374-9017)
Taha, Walid
Bartha, Ferenc A.
Duracz, Jan
Duracz, Adam
Ames, Aaron D.

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