---
_id: '8287'
abstract:
- lang: eng
  text: Reachability analysis aims at identifying states reachable by a system within
    a given time horizon. This task is known to be computationally expensive for linear
    hybrid systems. Reachability analysis works by iteratively applying continuous
    and discrete post operators to compute states reachable according to continuous
    and discrete dynamics, respectively. In this paper, we enhance both of these operators
    and make sure that most of the involved computations are performed in low-dimensional
    state space. In particular, we improve the continuous-post operator by performing
    computations in high-dimensional state space only for time intervals relevant
    for the subsequent application of the discrete-post operator. Furthermore, the
    new discrete-post operator performs low-dimensional computations by leveraging
    the structure of the guard and assignment of a considered transition. We illustrate
    the potential of our approach on a number of challenging benchmarks.
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergiy
  full_name: Bogomolov, Sergiy
  last_name: Bogomolov
- first_name: Marcelo
  full_name: Forets, Marcelo
  last_name: Forets
- first_name: Goran
  full_name: Frehse, Goran
  last_name: Frehse
- first_name: Kostiantyn
  full_name: Potomkin, Kostiantyn
  last_name: Potomkin
- first_name: Christian
  full_name: Schilling, Christian
  id: 3A2F4DCE-F248-11E8-B48F-1D18A9856A87
  last_name: Schilling
  orcid: 0000-0003-3658-1065
citation:
  ama: 'Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. Reachability analysis
    of linear hybrid systems via block decomposition. In: <i>Proceedings of the International
    Conference on Embedded Software</i>. ; 2020.'
  apa: Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., &#38; Schilling, C. (2020).
    Reachability analysis of linear hybrid systems via block decomposition. In <i>Proceedings
    of the International Conference on Embedded Software</i>. Virtual .
  chicago: Bogomolov, Sergiy, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, and
    Christian Schilling. “Reachability Analysis of Linear Hybrid Systems via Block
    Decomposition.” In <i>Proceedings of the International Conference on Embedded
    Software</i>, 2020.
  ieee: S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, and C. Schilling, “Reachability
    analysis of linear hybrid systems via block decomposition,” in <i>Proceedings
    of the International Conference on Embedded Software</i>, Virtual , 2020.
  ista: 'Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. 2020. Reachability
    analysis of linear hybrid systems via block decomposition. Proceedings of the
    International Conference on Embedded Software. EMSOFT: International Conference
    on Embedded Software.'
  mla: Bogomolov, Sergiy, et al. “Reachability Analysis of Linear Hybrid Systems via
    Block Decomposition.” <i>Proceedings of the International Conference on Embedded
    Software</i>, 2020.
  short: S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, C. Schilling, in:, Proceedings
    of the International Conference on Embedded Software, 2020.
conference:
  end_date: 2020-09-25
  location: 'Virtual '
  name: 'EMSOFT: International Conference on Embedded Software'
  start_date: 2020-09-20
date_created: 2020-08-24T12:56:20Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2023-08-22T13:27:32Z
ddc:
- '000'
department:
- _id: ToHe
ec_funded: 1
external_id:
  arxiv:
  - '1905.02458'
file:
- access_level: open_access
  checksum: d19e97d0f8a3a441dc078ec812297d75
  content_type: application/pdf
  creator: cschilli
  date_created: 2020-08-24T12:53:15Z
  date_updated: 2020-08-24T12:53:15Z
  file_id: '8288'
  file_name: 2020EMSOFT.pdf
  file_size: 696384
  relation: main_file
  success: 1
file_date_updated: 2020-08-24T12:53:15Z
has_accepted_license: '1'
keyword:
- reachability
- hybrid systems
- decomposition
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
oa: 1
oa_version: Preprint
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S 11407_N23
  name: Rigorous Systems Engineering
- _id: 25C5A090-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00312
  name: The Wittgenstein Prize
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the International Conference on Embedded Software
publication_status: published
quality_controlled: '1'
related_material:
  record:
  - id: '8790'
    relation: later_version
    status: public
status: public
title: Reachability analysis of linear hybrid systems via block decomposition
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '6035'
abstract:
- lang: eng
  text: 'We present JuliaReach, a toolbox for set-based reachability analysis of dynamical
    systems. JuliaReach consists of two main packages: Reachability, containing implementations
    of reachability algorithms for continuous and hybrid systems, and LazySets, a
    standalone library that implements state-of-the-art algorithms for calculus with
    convex sets. The library offers both concrete and lazy set representations, where
    the latter stands for the ability to delay set computations until they are needed.
    The choice of the programming language Julia and the accompanying documentation
    of our toolbox allow researchers to easily translate set-based algorithms from
    mathematics to software in a platform-independent way, while achieving runtime
    performance that is comparable to statically compiled languages. Combining lazy
    operations in high dimensions and explicit computations in low dimensions, JuliaReach
    can be applied to solve complex, large-scale problems.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergiy
  full_name: Bogomolov, Sergiy
  id: 369D9A44-F248-11E8-B48F-1D18A9856A87
  last_name: Bogomolov
  orcid: 0000-0002-0686-0365
- first_name: Marcelo
  full_name: Forets, Marcelo
  last_name: Forets
- first_name: Goran
  full_name: Frehse, Goran
  last_name: Frehse
- first_name: Kostiantyn
  full_name: Potomkin, Kostiantyn
  last_name: Potomkin
- first_name: Christian
  full_name: Schilling, Christian
  id: 3A2F4DCE-F248-11E8-B48F-1D18A9856A87
  last_name: Schilling
  orcid: 0000-0003-3658-1065
citation:
  ama: 'Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. JuliaReach: A toolbox
    for set-based reachability. In: <i>Proceedings of the 22nd International Conference
    on Hybrid Systems: Computation and Control</i>. Vol 22. ACM; 2019:39-44. doi:<a
    href="https://doi.org/10.1145/3302504.3311804">10.1145/3302504.3311804</a>'
  apa: 'Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., &#38; Schilling, C. (2019).
    JuliaReach: A toolbox for set-based reachability. In <i>Proceedings of the 22nd
    International Conference on Hybrid Systems: Computation and Control</i> (Vol.
    22, pp. 39–44). Montreal, QC, Canada: ACM. <a href="https://doi.org/10.1145/3302504.3311804">https://doi.org/10.1145/3302504.3311804</a>'
  chicago: 'Bogomolov, Sergiy, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin,
    and Christian Schilling. “JuliaReach: A Toolbox for Set-Based Reachability.” In
    <i>Proceedings of the 22nd International Conference on Hybrid Systems: Computation
    and Control</i>, 22:39–44. ACM, 2019. <a href="https://doi.org/10.1145/3302504.3311804">https://doi.org/10.1145/3302504.3311804</a>.'
  ieee: 'S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, and C. Schilling, “JuliaReach:
    A toolbox for set-based reachability,” in <i>Proceedings of the 22nd International
    Conference on Hybrid Systems: Computation and Control</i>, Montreal, QC, Canada,
    2019, vol. 22, pp. 39–44.'
  ista: 'Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. 2019. JuliaReach:
    A toolbox for set-based reachability. Proceedings of the 22nd International Conference
    on Hybrid Systems: Computation and Control. HSCC: Hybrid Systems Computation and
    Control vol. 22, 39–44.'
  mla: 'Bogomolov, Sergiy, et al. “JuliaReach: A Toolbox for Set-Based Reachability.”
    <i>Proceedings of the 22nd International Conference on Hybrid Systems: Computation
    and Control</i>, vol. 22, ACM, 2019, pp. 39–44, doi:<a href="https://doi.org/10.1145/3302504.3311804">10.1145/3302504.3311804</a>.'
  short: 'S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, C. Schilling, in:, Proceedings
    of the 22nd International Conference on Hybrid Systems: Computation and Control,
    ACM, 2019, pp. 39–44.'
conference:
  end_date: 2019-04-18
  location: Montreal, QC, Canada
  name: 'HSCC: Hybrid Systems Computation and Control'
  start_date: 2019-04-16
date_created: 2019-02-18T14:43:28Z
date_published: 2019-04-16T00:00:00Z
date_updated: 2023-08-24T14:47:21Z
day: '16'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1145/3302504.3311804
ec_funded: 1
external_id:
  arxiv:
  - '1901.10736'
  isi:
  - '000516713900005'
file:
- access_level: open_access
  checksum: 28ed56439aea5991c3122d4730fd828f
  content_type: application/pdf
  creator: cschilli
  date_created: 2019-03-05T09:27:18Z
  date_updated: 2020-07-14T12:47:17Z
  file_id: '6067'
  file_name: hscc19.pdf
  file_size: 3784414
  relation: main_file
file_date_updated: 2020-07-14T12:47:17Z
has_accepted_license: '1'
intvolume: '        22'
isi: 1
keyword:
- reachability analysis
- hybrid systems
- lazy computation
language:
- iso: eng
month: '04'
oa: 1
oa_version: Submitted Version
page: 39-44
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z211
  name: The Wittgenstein Prize
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S 11407_N23
  name: Rigorous Systems Engineering
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: 'Proceedings of the 22nd International Conference on Hybrid Systems:
  Computation and Control'
publication_identifier:
  isbn:
  - '9781450362825'
publication_status: published
publisher: ACM
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'JuliaReach: A toolbox for set-based reachability'
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2019'
...