Safety verification of nonlinear hybrid systems based on invariant clusters Kong, Hui ; https://orcid.org/0000-0002-3066-6941 Bogomolov, Sergiy ; https://orcid.org/0000-0002-0686-0365 Schilling, Christian Jiang, Yu Henzinger, Thomas A ; https://orcid.org/0000−0002−2985−7724 ddc:000 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. ACM 2017 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/663 https://research-explorer.ista.ac.at/download/663/4873 Kong H, Bogomolov S, Schilling C, Jiang Y, Henzinger TA. Safety verification of nonlinear hybrid systems based on invariant clusters. In: <i>Proceedings of the 20th International Conference on Hybrid Systems</i>. ACM; 2017:163-172. doi:<a href="https://doi.org/10.1145/3049797.3049814">10.1145/3049797.3049814</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/3049797.3049814 info:eu-repo/semantics/altIdentifier/isbn/978-145034590-3 info:eu-repo/semantics/altIdentifier/wos/000615962400019 info:eu-repo/semantics/openAccess