---
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_identifier:
  - UT:000615962400019
  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@
...