---
_id: '53101'
abstract:
- lang: eng
  text: In this work, we consider optimal control problems for mechanical systems
    with fixed initial and free final state and a quadratic Lagrange term. Specifically,
    the dynamics is described by a second order ODE containing an affine control term.
    Classically, Pontryagin's maximum principle gives necessary optimality conditions
    for the optimal control problem. For smooth problems, alternatively, a variational
    approach based on an augmented objective can be followed. Here, we propose a new
    Lagrangian approach leading to equivalent necessary optimality conditions in the
    form of Euler-Lagrange equations. Thus, the differential geometric structure (similar
    to classical Lagrangian dynamics) can be exploited in the framework of optimal
    control problems. In particular, the formulation enables the symplectic discretisation
    of the optimal control problem via variational integrators in a straightforward
    way.
article_type: original
author:
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- 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: Rodrigo T. Sato Martín de
  full_name: Almagro, Rodrigo T. Sato Martín de
  last_name: Almagro
- first_name: Flóra Orsolya
  full_name: Szemenyei, Flóra Orsolya
  last_name: Szemenyei
citation:
  ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO.
    A new Lagrangian approach to control affine systems with a quadratic Lagrange
    term. <i>Journal of Computational Dynamics</i>. 2024;0(0):0-0. doi:<a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>
  apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de,
    &#38; Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems
    with a quadratic Lagrange term. <i>Journal of Computational Dynamics</i>, <i>0</i>(0),
    0–0. <a href="https://doi.org/10.3934/jcd.2024017">https://doi.org/10.3934/jcd.2024017</a>
  bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A
    new Lagrangian approach to control affine systems with a quadratic Lagrange term},
    volume={0}, DOI={<a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>},
    number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute
    of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya,
    Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei,
    Flóra Orsolya}, year={2024}, pages={0–0} }'
  chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T.
    Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach
    to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Computational
    Dynamics</i> 0, no. 0 (2024): 0–0. <a href="https://doi.org/10.3934/jcd.2024017">https://doi.org/10.3934/jcd.2024017</a>.'
  ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro,
    and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with
    a quadratic Lagrange term,” <i>Journal of Computational Dynamics</i>, vol. 0,
    no. 0, pp. 0–0, 2024, doi: <a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>.'
  mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems
    with a Quadratic Lagrange Term.” <i>Journal of Computational Dynamics</i>, vol.
    0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:<a
    href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>.
  short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O.
    Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
  issn:
  - 2158-2491
  - 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
  term
type: journal_article
user_id: '87909'
volume: '0'
year: '2024'
...