---
_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'
...
---
_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'
...
---
_id: '9994'
abstract:
- lang: eng
  text: Reliability-adaptive systems allow an adaptation of system behavior based
    on current system reliability. They can extend their lifetime at the cost of lowered
    performance or vice versa. This can be used to adapt failure behavior according
    to a maintenance plan, thus increasing availability while using up system capability
    fully. To facilitate setup, a control algorithm independent of a degradation model
    is desired. A closed loop control technique for reliability based on a health
    index, a measure for system degradation, is introduced. It uses self-optimization
    as means to implement behavior adaptation. This is based on selecting the priorities
    of objectives that the system pursues. Possible working points are computed beforehand
    using model-based multiobjective optimization techniques. The controller selects
    the priorities of objectives and this way balances reliability and performance.
    As exemplary application, an automatically actuated single plate dry clutch is
    introduced. The entire reliability control is setup and lifetime experiments are
    conducted. Results show that the variance of time to failure is reduced greatly,
    making the failure behavior more predictable. At the same time, the desired usable
    lifetime can be extended at the cost of system performance to allow for changed
    maintenance intervals. Together, these possibilities allow for greater system
    usage and better planning of maintenance.
author:
- first_name: Tobias
  full_name: Meyer, Tobias
  last_name: Meyer
citation:
  ama: Meyer T. <i>Optimization-Based Reliability Control of Mechatronic Systems</i>.
    Shaker; 2018.
  apa: Meyer, T. (2018). <i>Optimization-based reliability control of mechatronic
    systems</i>. Shaker.
  bibtex: '@book{Meyer_2018, title={Optimization-based reliability control of mechatronic
    systems}, publisher={Shaker}, author={Meyer, Tobias}, year={2018} }'
  chicago: Meyer, Tobias. <i>Optimization-Based Reliability Control of Mechatronic
    Systems</i>. Shaker, 2018.
  ieee: T. Meyer, <i>Optimization-based reliability control of mechatronic systems</i>.
    Shaker, 2018.
  mla: Meyer, Tobias. <i>Optimization-Based Reliability Control of Mechatronic Systems</i>.
    Shaker, 2018.
  short: T. Meyer, Optimization-Based Reliability Control of Mechatronic Systems,
    Shaker, 2018.
date_created: 2019-05-27T10:21:17Z
date_updated: 2023-09-15T12:26:09Z
department:
- _id: '151'
keyword:
- dependability
- reliability
- behavior adaptation
- self-optimization
- multiobjective optimization
- optimal control
- automotive drivetrain
- clutch system
- reliability-adaptive system
language:
- iso: eng
publisher: Shaker
status: public
title: Optimization-based reliability control of mechatronic systems
type: dissertation
user_id: '210'
year: '2018'
...
---
_id: '9763'
abstract:
- lang: eng
  text: Recent advances in information processing enable new kinds of technical systems,
    called self-optimizing systems. These systems are able to adapt their objectives
    and their behavior according to the current situation and influences autonomously.
    This behavior adaptation is non-deterministic and hence self-optimization is a
    risk to the system, e.g. if the result of the self-optimization process does not
    match the suddenly changed situation. In contrary, self-optimization could be
    used to increase the dependability by pursuing objectives like reliability and
    availability. In our preceding publications we introduced the so called multi-level
    dependability concept to cope with this new kind of systems (cf. [6]). This concept
    comprises the monitoring of the system behavior, the classification of the current
    situation, and the selection of the appropriate measure, if reliability limits
    are exceeded. In this paper we present for the first time experimental results.
    The dependability concept is implemented in the self-optimizing active guidance
    system of a railway vehicle. The test drives illustrate clearly that the proposed
    concept is able to cope with, e.g., sensor failures, and is able to increase the
    reliability and availability of the active guidance module.
author:
- first_name: Christoph
  full_name: Sondermann-Wölke, Christoph
  last_name: Sondermann-Wölke
- first_name: Jens
  full_name: Geisler, Jens
  last_name: Geisler
- first_name: Walter
  full_name: Sextro, Walter
  id: '21220'
  last_name: Sextro
citation:
  ama: 'Sondermann-Wölke C, Geisler J, Sextro W. Increasing the reliability of a self-optimizing
    railway guidance system. In: <i>Reliability and Maintainability Symposium (RAMS),
    2010 Proceedings - Annual</i>. ; 2010:1-6. doi:<a href="https://doi.org/10.1109/RAMS.2010.5448080">10.1109/RAMS.2010.5448080</a>'
  apa: Sondermann-Wölke, C., Geisler, J., &#38; Sextro, W. (2010). Increasing the
    reliability of a self-optimizing railway guidance system. In <i>Reliability and
    Maintainability Symposium (RAMS), 2010 Proceedings - Annual</i> (pp. 1–6). <a
    href="https://doi.org/10.1109/RAMS.2010.5448080">https://doi.org/10.1109/RAMS.2010.5448080</a>
  bibtex: '@inproceedings{Sondermann-Wölke_Geisler_Sextro_2010, title={Increasing
    the reliability of a self-optimizing railway guidance system}, DOI={<a href="https://doi.org/10.1109/RAMS.2010.5448080">10.1109/RAMS.2010.5448080</a>},
    booktitle={Reliability and Maintainability Symposium (RAMS), 2010 Proceedings
    - Annual}, author={Sondermann-Wölke, Christoph and Geisler, Jens and Sextro, Walter},
    year={2010}, pages={1–6} }'
  chicago: Sondermann-Wölke, Christoph, Jens Geisler, and Walter Sextro. “Increasing
    the Reliability of a Self-Optimizing Railway Guidance System.” In <i>Reliability
    and Maintainability Symposium (RAMS), 2010 Proceedings - Annual</i>, 1–6, 2010.
    <a href="https://doi.org/10.1109/RAMS.2010.5448080">https://doi.org/10.1109/RAMS.2010.5448080</a>.
  ieee: C. Sondermann-Wölke, J. Geisler, and W. Sextro, “Increasing the reliability
    of a self-optimizing railway guidance system,” in <i>Reliability and Maintainability
    Symposium (RAMS), 2010 Proceedings - Annual</i>, 2010, pp. 1–6.
  mla: Sondermann-Wölke, Christoph, et al. “Increasing the Reliability of a Self-Optimizing
    Railway Guidance System.” <i>Reliability and Maintainability Symposium (RAMS),
    2010 Proceedings - Annual</i>, 2010, pp. 1–6, doi:<a href="https://doi.org/10.1109/RAMS.2010.5448080">10.1109/RAMS.2010.5448080</a>.
  short: 'C. Sondermann-Wölke, J. Geisler, W. Sextro, in: Reliability and Maintainability
    Symposium (RAMS), 2010 Proceedings - Annual, 2010, pp. 1–6.'
date_created: 2019-05-13T10:35:39Z
date_updated: 2022-01-06T07:04:19Z
department:
- _id: '151'
doi: 10.1109/RAMS.2010.5448080
keyword:
- availability
- dependability concept
- multilevel dependability concept
- railway vehicle
- reliability
- self optimizing active guidance system
- self optimizing railway guidance system
- situation classification
- system behavior monitoring
- optimal control
- railways
- reliability theory
- self-adjusting systems
language:
- iso: eng
page: 1 -6
publication: Reliability and Maintainability Symposium (RAMS), 2010 Proceedings -
  Annual
publication_identifier:
  issn:
  - 0149-144X
quality_controlled: '1'
status: public
title: Increasing the reliability of a self-optimizing railway guidance system
type: conference
user_id: '55222'
year: '2010'
...