--- res: bibo_abstract: - In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient. @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: Sergiy foaf_name: Bogomolov, Sergiy foaf_surname: Bogomolov orcid: 0000-0002-0686-0365 - foaf_Person: foaf_givenName: Christian foaf_name: Schilling, Christian foaf_surname: Schilling - foaf_Person: foaf_givenName: Yu foaf_name: Jiang, Yu foaf_surname: Jiang - 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: 10.1145/3049797.3049814 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/978-145034590-3 dct_language: eng dct_publisher: ACM@ dct_title: Safety verification of nonlinear hybrid systems based on invariant clusters@ ...