Safe & robust reachability analysis of hybrid systems
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 transi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/56209/ |
| _version_ | 1848799293627957248 |
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| author | Moggi, Eugenio Farjudian, Amin Duracz, Adam Taha, Walid |
| author_facet | Moggi, Eugenio Farjudian, Amin Duracz, Adam Taha, Walid |
| author_sort | Moggi, Eugenio |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:33:22Z |
| format | Article |
| id | nottingham-56209 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:33:22Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-562092019-03-04T09:51:29Z https://eprints.nottingham.ac.uk/56209/ Safe & robust reachability analysis of hybrid systems Moggi, Eugenio Farjudian, Amin Duracz, Adam Taha, Walid 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. Elsevier 2018-08-10 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/56209/1/2018-Moggi_Farjudian_Duracz_Taha-Safe_and_Robust_Reachability_Analysis_of_Hybrid_Systems-TCS.pdf 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 Hybrid systems; Reachability; Robustness; Domain theory https://www.sciencedirect.com/science/article/pii/S0304397518304365?via%3Dihub doi:10.1016/j.tcs.2018.06.020 doi:10.1016/j.tcs.2018.06.020 |
| spellingShingle | Hybrid systems; Reachability; Robustness; Domain theory Moggi, Eugenio Farjudian, Amin Duracz, Adam Taha, Walid Safe & robust reachability analysis of hybrid systems |
| title | Safe & robust reachability analysis of hybrid systems |
| title_full | Safe & robust reachability analysis of hybrid systems |
| title_fullStr | Safe & robust reachability analysis of hybrid systems |
| title_full_unstemmed | Safe & robust reachability analysis of hybrid systems |
| title_short | Safe & robust reachability analysis of hybrid systems |
| title_sort | safe & robust reachability analysis of hybrid systems |
| topic | Hybrid systems; Reachability; Robustness; Domain theory |
| url | https://eprints.nottingham.ac.uk/56209/ https://eprints.nottingham.ac.uk/56209/ https://eprints.nottingham.ac.uk/56209/ |