---
_id: '663'
abstract:
- lang: eng
  text: '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. '
author:
- first_name: Hui
  full_name: Kong, Hui
  id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87
  last_name: Kong
  orcid: 0000-0002-3066-6941
- first_name: Sergiy
  full_name: Bogomolov, Sergiy
  last_name: Bogomolov
  orcid: 0000-0002-0686-0365
- first_name: Christian
  full_name: Schilling, Christian
  last_name: Schilling
- first_name: Yu
  full_name: Jiang, Yu
  last_name: Jiang
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
citation:
  ama: '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>'
  apa: 'Kong, H., Bogomolov, S., Schilling, C., Jiang, Y., &#38; Henzinger, T. A.
    (2017). Safety verification of nonlinear hybrid systems based on invariant clusters.
    In <i>Proceedings of the 20th International Conference on Hybrid Systems</i> (pp.
    163–172). Pittsburgh, PA, United States: ACM. <a href="https://doi.org/10.1145/3049797.3049814">https://doi.org/10.1145/3049797.3049814</a>'
  chicago: Kong, Hui, Sergiy Bogomolov, Christian Schilling, Yu Jiang, and Thomas
    A Henzinger. “Safety Verification of Nonlinear Hybrid Systems Based on Invariant
    Clusters.” In <i>Proceedings of the 20th International Conference on Hybrid Systems</i>,
    163–72. ACM, 2017. <a href="https://doi.org/10.1145/3049797.3049814">https://doi.org/10.1145/3049797.3049814</a>.
  ieee: H. Kong, S. Bogomolov, C. Schilling, Y. Jiang, and T. A. Henzinger, “Safety
    verification of nonlinear hybrid systems based on invariant clusters,” in <i>Proceedings
    of the 20th International Conference on Hybrid Systems</i>, Pittsburgh, PA, United
    States, 2017, pp. 163–172.
  ista: 'Kong H, Bogomolov S, Schilling C, Jiang Y, Henzinger TA. 2017. Safety verification
    of nonlinear hybrid systems based on invariant clusters. Proceedings of the 20th
    International Conference on Hybrid Systems. HSCC: Hybrid Systems Computation and
    Control , 163–172.'
  mla: Kong, Hui, et al. “Safety Verification of Nonlinear Hybrid Systems Based on
    Invariant Clusters.” <i>Proceedings of the 20th International Conference on Hybrid
    Systems</i>, ACM, 2017, pp. 163–72, doi:<a href="https://doi.org/10.1145/3049797.3049814">10.1145/3049797.3049814</a>.
  short: H. Kong, S. Bogomolov, C. Schilling, Y. Jiang, T.A. Henzinger, in:, Proceedings
    of the 20th International Conference on Hybrid Systems, ACM, 2017, pp. 163–172.
conference:
  end_date: 2017-04-20
  location: Pittsburgh, PA, United States
  name: 'HSCC: Hybrid Systems Computation and Control '
  start_date: 2017-04-18
date_created: 2018-12-11T11:47:47Z
date_published: 2017-04-01T00:00:00Z
date_updated: 2021-01-12T08:08:17Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1145/3049797.3049814
file:
- access_level: open_access
  checksum: b7667434cbf5b5f0ade3bea1dbe5bf63
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:11:20Z
  date_updated: 2020-07-14T12:47:34Z
  file_id: '4873'
  file_name: IST-2017-817-v1+1_p163-kong.pdf
  file_size: 1650530
  relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Submitted Version
page: 163 - 172
publication: Proceedings of the 20th International Conference on Hybrid Systems
publication_identifier:
  isbn:
  - 978-145034590-3
publication_status: published
publisher: ACM
publist_id: '7067'
pubrep_id: '817'
quality_controlled: '1'
scopus_import: 1
status: public
title: Safety verification of nonlinear hybrid systems based on invariant clusters
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...