Safe & robust reachability analysis of hybrid systems

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Moggi, Eugenio, Farjudian, Amin, Duracz, Adam and Taha, Walid (2018) Safe & robust reachability analysis of hybrid systems. Theoretical Computer Science, 747 . pp. 75-99. ISSN 03043975

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Abstract

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.

Item Type: Article
Keywords: Hybrid systems; Reachability; Robustness; Domain theory
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1016/j.tcs.2018.06.020
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Depositing User: Yu, Tiffany
Date Deposited: 04 Mar 2019 09:51
Last Modified: 04 Mar 2019 09:51
URI: https://eprints.nottingham.ac.uk/id/eprint/56209

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