Computability of the Behaviour of Impacting Systems Beyond Zeno Times

P. Collins*, M. Konecny

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

Mathematical models of hybrid systems may exhibit Zeno behaviour, in which infinitely many discrete events occur in a finite time interval. Although this may be considered physically unrealistic, since Zeno behaviour is useful in modelling real-world systems, it is important for computational tools to be able to handle it. In particular, verification tools should use a well-defined semantics under which the Zeno behaviour is effectively and rigorously computable. In this paper, we give a semantics for systems with events similar to mechanical impacts and show that computation of the behaviour is possible, even beyond the Zeno time. If we allow perturbations outside this class of impacting systems, then it may not be possible to handle Zeno behaviour in a realistic way. Copyright (C) 2022 The Authors.
Original languageEnglish
Title of host publicationIFAC PAPERSONLINE
PublisherElsevier
Pages85-90
Number of pages6
Volume55
Edition30
DOIs
Publication statusPublished - 2022
Event25th International Symposium on Mathematical Theory of Networks and Systems (MTNS) - University of Bayreuth, Bayreuth, Germany
Duration: 12 Sept 202216 Sept 2022
https://www.mtns2022.uni-bayreuth.de/en/index.html

Symposium

Symposium25th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Abbreviated titleMTNS 2022
Country/TerritoryGermany
CityBayreuth
Period12/09/2216/09/22
Internet address

Keywords

  • Hybrid system
  • Zeno
  • impact
  • computability
  • transfinite
  • HYBRID
  • STABILITY

Cite this