---
_id: '63557'
abstract:
- lang: eng
  text: We discretise a recently proposed new Lagrangian approach to optimal control
    problems with dynamics described by force-controlled Euler-Lagrange equations
    (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are
    in the form of discrete Lagrangians. We show that the discrete necessary conditions
    for optimality obtained provide variational integrators for the continuous problem,
    akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This
    approach paves the way for the use of variational error analysis to derive the
    order of convergence of the resulting numerical schemes for both state and costate
    variables and to apply discrete Noether’s theorem to compute conserved quantities,
    distinguishing itself from existing geometric approaches. We show for a family
    of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’,
    meaning they yield forced symplectic integrators for the underlying controlled
    mechanical system and overall symplectic integrators in the state-adjoint space.
    Multi-body dynamics examples are solved numerically using the new approach. In
    addition, the new approach is compared to standard direct approaches in terms
    of computational performance and error convergence. The results highlight the
    advantages of the new approach, namely, better performance and convergence behaviour
    of state and costate variables consistent with variational error analysis and
    automatic preservation of certain first integrals.
author:
- first_name: Michael
  full_name: Konopik, Michael
  last_name: Konopik
- 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.
  full_name: Sato Martín de Almagro, Rodrigo T.
  last_name: Sato Martín de Almagro
citation:
  ama: Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro
    RT. On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics. <i>Multibody System Dynamics</i>. Published online 2026.
    doi:<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>
  apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; Sato Martín de Almagro,
    R. T. (2026). On the variational discretisation of optimal control problems for
    unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. <a href="https://doi.org/10.1007/s11044-025-10138-1">https://doi.org/10.1007/s11044-025-10138-1</a>
  bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026,
    title={On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics}, DOI={<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>},
    journal={Multibody System Dynamics}, publisher={Springer Science and Business
    Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya,
    Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026}
    }'
  chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum,
    and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal
    Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>,
    2026. <a href="https://doi.org/10.1007/s11044-025-10138-1">https://doi.org/10.1007/s11044-025-10138-1</a>.
  ieee: 'M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro,
    “On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics,” <i>Multibody System Dynamics</i>, 2026, doi: <a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>.'
  mla: Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control
    Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>,
    Springer Science and Business Media LLC, 2026, doi:<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>.
  short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro,
    Multibody System Dynamics (2026).
date_created: 2026-01-12T11:33:54Z
date_updated: 2026-01-12T11:35:27Z
department:
- _id: '636'
doi: 10.1007/s11044-025-10138-1
language:
- iso: eng
publication: Multibody System Dynamics
publication_identifier:
  issn:
  - 1384-5640
  - 1573-272X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the variational discretisation of optimal control problems for unconstrained
  Lagrangian dynamics
type: journal_article
user_id: '87909'
year: '2026'
...