---
_id: '9103'
abstract:
- lang: eng
  text: 'We introduce LRT-NG, a set of techniques and an associated toolset that computes
    a reachtube (an over-approximation of the set of reachable states over a given
    time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the
    state-of-the-art Langrangian Reachability and its associated tool LRT. From a
    theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses
    for the first time an analytically computed metric for the propagated ball which
    is proven to minimize the ball’s volume. We emphasize that the metric computation
    is the centerpiece of all bloating-based techniques. Secondly, it computes the
    next reachset as the intersection of two balls: one based on the Cartesian metric
    and the other on the new metric. While the two metrics were previously considered
    opposing approaches, their joint use considerably tightens the reachtubes. Thirdly,
    it avoids the "wrapping effect" associated with the validated integration of the
    center of the reachset, by optimally absorbing the interval approximation in the
    radius of the next ball. From a tool-development perspective, LRT-NG is superior
    to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD.
    This required the implementation of the Lohner method and a Runge-Kutta time-propagation
    method. Secondly, it has an improved interface, allowing the input model and initial
    conditions to be provided as external input files. Our experiments on a comprehensive
    set of benchmarks, including two Neural ODEs, demonstrates LRT-NG’s superior performance
    compared to LRT, CAPD, and Flow*.'
acknowledgement: "The authors would like to thank Ramin Hasani and Guillaume Berger
  for intellectual discussions about the research which lead to the generation of
  new ideas. ML was supported in part by the Austrian Science Fund (FWF) under grant
  Z211-N23 (Wittgenstein Award). Smolka’s research was supported by NSF grants CPS-1446832
  and CCF-1918225. Gruenbacher is funded by FWF project W1255-N23. JC was partially
  supported by NAWA Polish Returns grant\r\nPPN/PPO/2018/1/00029.\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Sophie
  full_name: Gruenbacher, Sophie
  last_name: Gruenbacher
- first_name: Jacek
  full_name: Cyranka, Jacek
  last_name: Cyranka
- first_name: Mathias
  full_name: Lechner, Mathias
  id: 3DC22916-F248-11E8-B48F-1D18A9856A87
  last_name: Lechner
- first_name: Md Ariful
  full_name: Islam, Md Ariful
  last_name: Islam
- first_name: Scott A.
  full_name: Smolka, Scott A.
  last_name: Smolka
- first_name: Radu
  full_name: Grosu, Radu
  last_name: Grosu
citation:
  ama: 'Gruenbacher S, Cyranka J, Lechner M, Islam MA, Smolka SA, Grosu R. Lagrangian
    reachtubes: The next generation. In: <i>Proceedings of the 59th IEEE Conference
    on Decision and Control</i>. Vol 2020. IEEE; 2020:1556-1563. doi:<a href="https://doi.org/10.1109/CDC42340.2020.9304042">10.1109/CDC42340.2020.9304042</a>'
  apa: 'Gruenbacher, S., Cyranka, J., Lechner, M., Islam, M. A., Smolka, S. A., &#38;
    Grosu, R. (2020). Lagrangian reachtubes: The next generation. In <i>Proceedings
    of the 59th IEEE Conference on Decision and Control</i> (Vol. 2020, pp. 1556–1563).
    Jeju Islang, Korea (South): IEEE. <a href="https://doi.org/10.1109/CDC42340.2020.9304042">https://doi.org/10.1109/CDC42340.2020.9304042</a>'
  chicago: 'Gruenbacher, Sophie, Jacek Cyranka, Mathias Lechner, Md Ariful Islam,
    Scott A. Smolka, and Radu Grosu. “Lagrangian Reachtubes: The next Generation.”
    In <i>Proceedings of the 59th IEEE Conference on Decision and Control</i>, 2020:1556–63.
    IEEE, 2020. <a href="https://doi.org/10.1109/CDC42340.2020.9304042">https://doi.org/10.1109/CDC42340.2020.9304042</a>.'
  ieee: 'S. Gruenbacher, J. Cyranka, M. Lechner, M. A. Islam, S. A. Smolka, and R.
    Grosu, “Lagrangian reachtubes: The next generation,” in <i>Proceedings of the
    59th IEEE Conference on Decision and Control</i>, Jeju Islang, Korea (South),
    2020, vol. 2020, pp. 1556–1563.'
  ista: 'Gruenbacher S, Cyranka J, Lechner M, Islam MA, Smolka SA, Grosu R. 2020.
    Lagrangian reachtubes: The next generation. Proceedings of the 59th IEEE Conference
    on Decision and Control. CDC: Conference on Decision and Control vol. 2020, 1556–1563.'
  mla: 'Gruenbacher, Sophie, et al. “Lagrangian Reachtubes: The next Generation.”
    <i>Proceedings of the 59th IEEE Conference on Decision and Control</i>, vol. 2020,
    IEEE, 2020, pp. 1556–63, doi:<a href="https://doi.org/10.1109/CDC42340.2020.9304042">10.1109/CDC42340.2020.9304042</a>.'
  short: S. Gruenbacher, J. Cyranka, M. Lechner, M.A. Islam, S.A. Smolka, R. Grosu,
    in:, Proceedings of the 59th IEEE Conference on Decision and Control, IEEE, 2020,
    pp. 1556–1563.
conference:
  end_date: 2020-12-18
  location: Jeju Islang, Korea (South)
  name: 'CDC: Conference on Decision and Control'
  start_date: 2020-12-14
date_created: 2021-02-07T23:01:14Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-02-09T09:20:58Z
day: '14'
department:
- _id: ToHe
doi: 10.1109/CDC42340.2020.9304042
external_id:
  arxiv:
  - '2012.07458'
intvolume: '      2020'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2012.07458
month: '12'
oa: 1
oa_version: Preprint
page: 1556-1563
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z211
  name: The Wittgenstein Prize
publication: Proceedings of the 59th IEEE Conference on Decision and Control
publication_identifier:
  isbn:
  - '9781728174471'
  issn:
  - '07431546'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Lagrangian reachtubes: The next generation'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2020
year: '2020'
...