{"abstract":[{"text":"We address the problem of analyzing the reachable set of a polynomial nonlinear continuous system by over-approximating the flowpipe of its dynamics. The common approach to tackle this problem is to perform a numerical integration over a given time horizon based on Taylor expansion and interval arithmetic. However, this method results to be very conservative when there is a large difference in speed between trajectories as time progresses. In this paper, we propose to use combinations of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse box which is big enough to contain the segment is constructed using sampled simulation and then in the box we compute by linear programming a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe. The benefit of using PBT is that (1) BT is independent of time and hence can avoid being stretched and deformed by time; and (2) a small number of BTs can form a tight over-approximation for the flowpipe, which means that the computation required to decide whether the BTs intersect the unsafe set can be reduced significantly. We implemented a prototype called PBTS in C++. Experiments on some benchmark systems show that our approach is effective.","lang":"eng"}],"day":"18","quality_controlled":"1","file_date_updated":"2020-07-14T12:44:53Z","has_accepted_license":"1","scopus_import":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_created":"2018-12-11T11:44:51Z","oa":1,"_id":"142","license":"https://creativecommons.org/licenses/by/4.0/","ddc":["000"],"title":"Reachable set over-approximation for nonlinear systems using piecewise barrier tubes","article_processing_charge":"No","language":[{"iso":"eng"}],"date_published":"2018-07-18T00:00:00Z","alternative_title":["LNCS"],"author":[{"orcid":"0000-0002-3066-6941","first_name":"Hui","last_name":"Kong","full_name":"Kong, Hui","id":"3BDE25AA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bartocci, Ezio","first_name":"Ezio","last_name":"Bartocci"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","last_name":"Henzinger","orcid":"0000−0002−2985−7724"}],"status":"public","publist_id":"7781","publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-15T12:12:08Z","volume":10981,"external_id":{"isi":["000491481600024"]},"page":"449 - 467","project":[{"grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering"},{"_id":"25F42A32-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z211","name":"The Wittgenstein Prize"}],"file":[{"relation":"main_file","creator":"dernst","file_id":"5718","date_created":"2018-12-17T15:57:06Z","content_type":"application/pdf","access_level":"open_access","file_name":"2018_LNCS_Kong.pdf","date_updated":"2020-07-14T12:44:53Z","checksum":"fd95e8026deacef3dc752a733bb9355f","file_size":5591566}],"oa_version":"Published Version","acknowledgement":"Austrian Science Fund FWF: S11402-N23, S11405-N23, Z211-N32","type":"conference","month":"07","citation":{"apa":"Kong, H., Bartocci, E., &#38; Henzinger, T. A. (2018). Reachable set over-approximation for nonlinear systems using piecewise barrier tubes (Vol. 10981, pp. 449–467). Presented at the CAV: Computer Aided Verification, Oxford, United Kingdom: Springer. <a href=\"https://doi.org/10.1007/978-3-319-96145-3_24\">https://doi.org/10.1007/978-3-319-96145-3_24</a>","mla":"Kong, Hui, et al. <i>Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes</i>. Vol. 10981, Springer, 2018, pp. 449–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-96145-3_24\">10.1007/978-3-319-96145-3_24</a>.","ista":"Kong H, Bartocci E, Henzinger TA. 2018. Reachable set over-approximation for nonlinear systems using piecewise barrier tubes. CAV: Computer Aided Verification, LNCS, vol. 10981, 449–467.","ieee":"H. Kong, E. Bartocci, and T. A. Henzinger, “Reachable set over-approximation for nonlinear systems using piecewise barrier tubes,” presented at the CAV: Computer Aided Verification, Oxford, United Kingdom, 2018, vol. 10981, pp. 449–467.","short":"H. Kong, E. Bartocci, T.A. Henzinger, in:, Springer, 2018, pp. 449–467.","chicago":"Kong, Hui, Ezio Bartocci, and Thomas A Henzinger. “Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes,” 10981:449–67. Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-319-96145-3_24\">https://doi.org/10.1007/978-3-319-96145-3_24</a>.","ama":"Kong H, Bartocci E, Henzinger TA. Reachable set over-approximation for nonlinear systems using piecewise barrier tubes. In: Vol 10981. Springer; 2018:449-467. doi:<a href=\"https://doi.org/10.1007/978-3-319-96145-3_24\">10.1007/978-3-319-96145-3_24</a>"},"publication_status":"published","department":[{"_id":"ToHe"}],"year":"2018","doi":"10.1007/978-3-319-96145-3_24","isi":1,"intvolume":"     10981","conference":{"end_date":"2018-07-17","name":"CAV: Computer Aided Verification","start_date":"2018-07-14","location":"Oxford, United Kingdom"}}