Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point. (May 2016)

• Record Type: Journal Article
• Authors: Konečný, Michal; Taha, Walid; Bartha, Ferenc A.; Duracz, Jan; Duracz, Adam; Ames, Aaron D.
• Is Part Of: Nonlinear analysis. Volume 20(2016)
• Page Start: 1
• Page End: 20
• Publication Date: 2016-05
• Subjects: Hybrid automata -- Zeno behavior -- Hybrid systems -- Rigorous computations -- Validated numerics; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2015.10.004
• Languages: English
• ISSNs: 1751-570X

Abstract

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.