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Safe & robust reachability analysis of hybrid systems
DIBRIS, Genova Univ., v. Dodecaneso 35, Genova, 16146, Italy.
University of Nottingham Ningbo, China.
Rice University, Houston, TX, United States.
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).ORCID iD: 0000-0003-3160-9188
2018 (English)In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 747, p. 75-99Article in journal (Refereed) Published
Abstract [en]

Hybrid systems—more precisely, their mathematical models—can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability—namely, the reflexive and transitive closure of a transition relation—can be unsafe, i.e., it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust w.r.t. small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation. © 2018 The Authors

Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2018. Vol. 747, p. 75-99
Keywords [en]
Computational methods, Computer science, Robustness (control systems), Continuous approximations, Domain theory, Reachability, Reachability analysis, Robust approximations, Small perturbations, Transition relations, Transitive closure, Hybrid systems
National Category
Control Engineering Computational Mathematics Embedded Systems
Identifiers
URN: urn:nbn:se:hh:diva-38699DOI: 10.1016/j.tcs.2018.06.020ISI: 000447571900005Scopus ID: 2-s2.0-85048949865OAI: oai:DiVA.org:hh-38699DiVA, id: diva2:1276475
Funder
Knowledge FoundationELLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Note

Funding: US NSF Grant number: 1736759

Available from: 2019-01-08 Created: 2019-01-08 Last updated: 2019-01-08Bibliographically approved

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Taha, Walid

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