---
_id: '58953'
abstract:
- lang: eng
  text: In this article, we investigate symmetry properties of distributed systems
    of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze
    their collective Fsync dynamics using of equivariant dynamical systems theory.
    To this end, we show that the corresponding evolution function commutes with rotational
    and reflective transformations of R^2. These form a group that is isomorphic to
    O(2) x S_n, the product group of the orthogonal group and the permutation on n
    elements. The theory of equivariant dynamical systems is used to deduce a hierarchy
    along which symmetries of a robot swarm can potentially increase following an
    arbitrary protocol. By decoupling the Look phase from the Compute and Move phases
    in the mathematical description of an LCM cycle, this hierarchy can be characterized
    in terms of automorphisms of connectivity graphs. In particular, we find all possible
    types of symmetry increase, if the decoupled Compute and Move phase is invertible.
    Finally, we apply our results to protocols which induce state-dependent linear
    dynamics, where the reduced system consisting of only the Compute and Move phase
    is linear.
author:
- first_name: Raphael
  full_name: Gerlach, Raphael
  id: '32655'
  last_name: Gerlach
  orcid: 0009-0002-4750-2051
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
citation:
  ama: Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots
    Using Equivariant  Dynamical Systems. <i>arXiv:250307576</i>. Published online
    2025.
  apa: Gerlach, R., &#38; von der Gracht, S. (2025). Analyzing Symmetries of Swarms
    of Mobile Robots Using Equivariant  Dynamical Systems. In <i>arXiv:2503.07576</i>.
  bibtex: '@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms
    of Mobile Robots Using Equivariant  Dynamical Systems}, journal={arXiv:2503.07576},
    author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }'
  chicago: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
    of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>,
    2025.
  ieee: R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile
    Robots Using Equivariant  Dynamical Systems,” <i>arXiv:2503.07576</i>. 2025.
  mla: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
    of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>,
    2025.
  short: R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).
date_created: 2025-03-11T08:21:05Z
date_updated: 2025-03-11T08:53:02Z
ddc:
- '004'
department:
- _id: '101'
external_id:
  arxiv:
  - '2503.07576'
file:
- access_level: open_access
  content_type: application/pdf
  creator: svdg
  date_created: 2025-03-11T08:27:32Z
  date_updated: 2025-03-11T08:27:32Z
  file_id: '58954'
  file_name: Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf
  file_size: 812198
  relation: main_file
file_date_updated: 2025-03-11T08:27:32Z
has_accepted_license: '1'
keyword:
- dynamical systems
- coupled systems
- distributed computing
- robot swarms
- autonomous mobile robots
- symmetry
- equivariant dynamics
language:
- iso: eng
oa: '1'
page: '23'
project:
- _id: '106'
  grant_number: '453112019'
  name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: arXiv:2503.07576
status: public
title: Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical
  Systems
type: preprint
user_id: '97359'
year: '2025'
...
---
_id: '57472'
abstract:
- lang: eng
  text: In this paper we introduce, in a Hilbert space setting, a second order dynamical
    system with asymptotically vanishing damping and vanishing Tikhonov regularization
    that approaches a multiobjective optimization problem with convex and differentiable
    components of the objective function. Trajectory solutions are shown to exist
    in finite dimensions. We prove fast convergence of the function values, quantified
    in terms of a merit function. Based on the regime considered, we establish both
    weak and, in some cases, strong convergence of trajectory solutions toward a weak
    Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually
    to each component of the objective function. This work extends results from single
    objective convex optimization into the multiobjective setting.
author:
- first_name: Radu Ioan
  full_name: Bot, Radu Ioan
  last_name: Bot
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
citation:
  ama: Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization
    for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>.
    Published online 2025.
  apa: Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov
    regularization for multobjective optimization. <i>Journal of Mathematical Analysis
    and Applications</i>.
  bibtex: '@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov
    regularization for multobjective optimization}, journal={Journal of Mathematical
    Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025}
    }'
  chicago: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing
    Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical
    Analysis and Applications</i>, 2025.
  ieee: R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization
    for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>,
    2025.
  mla: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov
    Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis
    and Applications</i>, 2025.
  short: R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).
date_created: 2024-11-28T08:58:17Z
date_updated: 2025-10-16T11:56:36Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
external_id:
  arxiv:
  - '2411.18422'
file:
- access_level: open_access
  content_type: application/pdf
  creator: sonntagk
  date_created: 2024-11-28T08:58:00Z
  date_updated: 2024-11-28T08:58:00Z
  file_id: '57473'
  file_name: Inertial dynamics with vanishing Tikhonov regularization for multobjective
    optimization.pdf
  file_size: 4291134
  relation: main_file
file_date_updated: 2024-11-28T08:58:00Z
has_accepted_license: '1'
keyword:
- Pareto optimization
- Lyapunov analysis
- gradient-like dynamical systems
- inertial dynamics
- asymptotic vanishing damping
- Tikhonov regularization
- strong convergence
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
main_file_link:
- url: https://arxiv.org/pdf/2411.18422
oa: '1'
publication: Journal of Mathematical Analysis and Applications
status: public
title: Inertial dynamics with vanishing Tikhonov regularization for multobjective
  optimization
type: journal_article
user_id: '56399'
year: '2025'
...
---
_id: '31066'
abstract:
- lang: eng
  text: 'While trade-offs between modeling effort and model accuracy remain a major
    concern with system identification, resorting to data-driven methods often leads
    to a complete disregard for physical plausibility. To address this issue, we propose
    a physics-guided hybrid approach for modeling non-autonomous systems under control.
    Starting from a traditional physics-based model, this is extended by a recurrent
    neural network and trained using a sophisticated multi-objective strategy yielding
    physically plausible models. While purely data-driven methods fail to produce
    satisfying results, experiments conducted on real data reveal substantial accuracy
    improvements by our approach compared to a physics-based model. '
author:
- first_name: Oliver
  full_name: Schön, Oliver
  last_name: Schön
- first_name: Ricarda-Samantha
  full_name: Götte, Ricarda-Samantha
  id: '43992'
  last_name: Götte
- first_name: Julia
  full_name: Timmermann, Julia
  id: '15402'
  last_name: Timmermann
citation:
  ama: 'Schön O, Götte R-S, Timmermann J. Multi-Objective Physics-Guided Recurrent
    Neural Networks for Identifying Non-Autonomous Dynamical Systems. In: <i>14th
    IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>. Vol 55.
    ; 2022:19-24. doi:<a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>'
  apa: Schön, O., Götte, R.-S., &#38; Timmermann, J. (2022). Multi-Objective Physics-Guided
    Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems. <i>14th
    IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>, <i>55</i>(12),
    19–24. <a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>
  bibtex: '@inproceedings{Schön_Götte_Timmermann_2022, title={Multi-Objective Physics-Guided
    Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems}, volume={55},
    DOI={<a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>},
    number={12}, booktitle={14th IFAC Workshop on Adaptive and Learning Control Systems
    (ALCOS 2022)}, author={Schön, Oliver and Götte, Ricarda-Samantha and Timmermann,
    Julia}, year={2022}, pages={19–24} }'
  chicago: Schön, Oliver, Ricarda-Samantha Götte, and Julia Timmermann. “Multi-Objective
    Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical
    Systems.” In <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS
    2022)</i>, 55:19–24, 2022. <a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>.
  ieee: 'O. Schön, R.-S. Götte, and J. Timmermann, “Multi-Objective Physics-Guided
    Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems,” in
    <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>,
    Casablanca, Morocco, 2022, vol. 55, no. 12, pp. 19–24, doi: <a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>.'
  mla: Schön, Oliver, et al. “Multi-Objective Physics-Guided Recurrent Neural Networks
    for Identifying Non-Autonomous Dynamical Systems.” <i>14th IFAC Workshop on Adaptive
    and Learning Control Systems (ALCOS 2022)</i>, vol. 55, no. 12, 2022, pp. 19–24,
    doi:<a href="https://doi.org/10.1016/j.ifacol.2022.07.282">https://doi.org/10.1016/j.ifacol.2022.07.282</a>.
  short: 'O. Schön, R.-S. Götte, J. Timmermann, in: 14th IFAC Workshop on Adaptive
    and Learning Control Systems (ALCOS 2022), 2022, pp. 19–24.'
conference:
  end_date: 2022-07-01
  location: Casablanca, Morocco
  name: 14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)
  start_date: 2022-06-29
date_created: 2022-05-05T06:22:55Z
date_updated: 2024-11-13T08:43:16Z
department:
- _id: '153'
- _id: '880'
doi: https://doi.org/10.1016/j.ifacol.2022.07.282
intvolume: '        55'
issue: '12'
keyword:
- neural networks
- physics-guided
- data-driven
- multi-objective optimization
- system identification
- machine learning
- dynamical systems
language:
- iso: eng
page: 19-24
publication: 14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)
quality_controlled: '1'
status: public
title: Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous
  Dynamical Systems
type: conference
user_id: '43992'
volume: 55
year: '2022'
...