---
_id: '59792'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by mechanical
    systems with symmetries, we focus on optimal control problems possessing certain
    symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788
    2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized
    the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic>
    we extend the <jats:italic>exponential turnpike property</jats:italic> to the
    <jats:italic>exponential trim turnpike</jats:italic> for control systems with
    symmetries induced by abelian or non-abelian groups. Our analysis is mainly based
    on the geometric reduction of control systems with symmetries. More concretely,
    we first reduce the control system on the quotient space and state the turnpike
    theorem for the reduced problem. Then we use the group properties to obtain the
    <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally,
    we illustrate our results on the Kepler problem and the rigid body problem.\r\n</jats:p>"
author:
- first_name: Kathrin
  full_name: Flaßkamp, Kathrin
  last_name: Flaßkamp
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
citation:
  ama: Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for
    optimal control problems with symmetries. <i>Mathematics of Control, Signals,
    and Systems</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>
  apa: Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025).
    Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of
    Control, Signals, and Systems</i>. <a href="https://doi.org/10.1007/s00498-025-00408-w">https://doi.org/10.1007/s00498-025-00408-w</a>
  bibtex: '@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim
    turnpikes for optimal control problems with symmetries}, DOI={<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>},
    journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science
    and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and
    Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }'
  chicago: Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar
    Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics
    of Control, Signals, and Systems</i>, 2025. <a href="https://doi.org/10.1007/s00498-025-00408-w">https://doi.org/10.1007/s00498-025-00408-w</a>.
  ieee: 'K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim
    turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control,
    Signals, and Systems</i>, 2025, doi: <a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>.'
  mla: Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with
    Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science
    and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>.
  short: K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics
    of Control, Signals, and Systems (2025).
date_created: 2025-05-05T09:23:38Z
date_updated: 2025-05-05T09:24:09Z
department:
- _id: '636'
doi: 10.1007/s00498-025-00408-w
language:
- iso: eng
publication: Mathematics of Control, Signals, and Systems
publication_identifier:
  issn:
  - 0932-4194
  - 1435-568X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Trim turnpikes for optimal control problems with symmetries
type: journal_article
user_id: '87909'
year: '2025'
...