---
_id: '22894'
abstract:
- lang: eng
  text: "The first order optimality conditions of optimal control problems (OCPs)
    can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational
    or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong
    term behaviour. As boundary value problems are posed on intervals of\r\nfixed,
    moderate length, it is not immediately clear whether methods can profit\r\nfrom
    structure preservation in this context. When parameters are present,\r\nsolutions
    can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate
    one another as parameters are varied. We will show that generic\r\nbifurcations
    of an OCP are preserved under discretisation when the OCP is\r\neither directly
    discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian
    boundary value problem using first order necessary\r\nconditions of optimality
    which is then solved using a symplectic integrator\r\n(indirect method). Moreover,
    certain bifurcations break when a non-symplectic\r\nscheme is used. The general
    phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid."
author:
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal
    control problems. 2021;54(19):334-339. doi:<a href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>
  apa: 'Offen, C., &#38; Ober-Blöbaum, S. (2021). <i>Bifurcation preserving discretisations
    of optimal control problems: Vol. 54(19)</i> (pp. 334–339). <a href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>'
  bibtex: '@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation
    preserving discretisations of optimal control problems}, volume={54(19)}, DOI={<a
    href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>},
    author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339},
    collection={IFAC-PapersOnLine} }'
  chicago: Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations
    of Optimal Control Problems.” IFAC-PapersOnLine, 2021. <a href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.
  ieee: 'C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of
    optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: <a href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.'
  mla: Offen, Christian, and Sina Ober-Blöbaum. <i>Bifurcation Preserving Discretisations
    of Optimal Control Problems</i>. 2021, pp. 334–39, doi:<a href="https://doi.org/10.1016/j.ifacol.2021.11.099">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.
  short: C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.
conference:
  end_date: 2021-10-13
  location: Berlin, Germany
  name: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control,
    LHMNC 2021
  start_date: 2021-10-11
date_created: 2021-07-29T09:38:32Z
date_updated: 2023-11-29T10:19:41Z
ddc:
- '510'
department:
- _id: '636'
doi: https://doi.org/10.1016/j.ifacol.2021.11.099
external_id:
  arxiv:
  - '2107.13853'
file:
- access_level: open_access
  content_type: application/pdf
  creator: coffen
  date_created: 2021-07-29T09:37:49Z
  date_updated: 2021-07-29T09:37:49Z
  file_id: '22895'
  file_name: ifacconf.pdf
  file_size: 3125220
  relation: main_file
file_date_updated: 2021-07-29T09:37:49Z
has_accepted_license: '1'
keyword:
- optimal control
- catastrophe theory
- bifurcations
- variational methods
- symplectic integrators
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.sciencedirect.com/science/article/pii/S2405896321021236
oa: '1'
page: 334-339
publication_identifier:
  issn:
  - 2405-8963
publication_status: published
quality_controlled: '1'
related_material:
  link:
  - description: GitHub/Zenodo
    relation: software
    url: https://doi.org/10.5281/zenodo.4562664
series_title: IFAC-PapersOnLine
status: public
title: Bifurcation preserving discretisations of optimal control problems
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...