--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Hui foaf_name: Kong, Hui foaf_surname: Kong foaf_workInfoHomepage: http://www.librecat.org/personId=3BDE25AA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-3066-6941 - foaf_Person: foaf_givenName: Ezio foaf_name: Bartocci, Ezio foaf_surname: Bartocci - foaf_Person: foaf_givenName: Thomas A foaf_name: Henzinger, Thomas A foaf_surname: Henzinger foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87 orcid: 0000−0002−2985−7724 bibo_doi: 10.1007/978-3-319-96145-3_24 bibo_volume: 10981 dct_date: 2018^xs_gYear dct_identifier: - UT:000491481600024 dct_language: eng dct_publisher: Springer@ dct_title: Reachable set over-approximation for nonlinear systems using piecewise barrier tubes@ ...