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Exponential and practical exponential stability of second-order formation control systems

Suttner, Raik and Sun, Zhiyong LU (2020) 58th IEEE Conference on Decision and Control, CDC 2019 In Proceedings of the IEEE Conference on Decision and Control 2019-December. p.3521-3526
Abstract

We study the problem of distance-based formation shape control for autonomous agents with double-integrator dynamics. Our considerations are focused on exponential stability properties. For second-order formation systems under the standard gradient-based control law, we prove local exponential stability with respect to the total energy by applying Chetaev's trick to the Lyapunov candidate function. We also propose a novel formation control law, which does not require measurements of relative positions but instead measurements of distances. The distance-only control law is based on an approximation of symmetric products of vector fields by sinusoidal perturbations. A suitable averaging analysis reveals that the averaged system coincides... (More)

We study the problem of distance-based formation shape control for autonomous agents with double-integrator dynamics. Our considerations are focused on exponential stability properties. For second-order formation systems under the standard gradient-based control law, we prove local exponential stability with respect to the total energy by applying Chetaev's trick to the Lyapunov candidate function. We also propose a novel formation control law, which does not require measurements of relative positions but instead measurements of distances. The distance-only control law is based on an approximation of symmetric products of vector fields by sinusoidal perturbations. A suitable averaging analysis reveals that the averaged system coincides with the multi-agent system under the standard gradient-based control law. This allows us to prove practical exponential stability for the system under the distance-only control law.

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Please use this url to cite or link to this publication:
author
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organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2019 IEEE 58th Conference on Decision and Control, CDC 2019
series title
Proceedings of the IEEE Conference on Decision and Control
volume
2019-December
article number
9030064
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
58th IEEE Conference on Decision and Control, CDC 2019
conference location
Nice, France
conference dates
2019-12-11 - 2019-12-13
external identifiers
  • scopus:85082469748
ISSN
2576-2370
0743-1546
ISBN
978-1-7281-1399-9
9781728113982
DOI
10.1109/CDC40024.2019.9030064
language
English
LU publication?
yes
id
851e16e9-dd44-44b0-a7fb-a14d065a8be1
date added to LUP
2020-04-29 15:20:43
date last changed
2024-02-16 14:20:26
@inproceedings{851e16e9-dd44-44b0-a7fb-a14d065a8be1,
  abstract     = {{<p>We study the problem of distance-based formation shape control for autonomous agents with double-integrator dynamics. Our considerations are focused on exponential stability properties. For second-order formation systems under the standard gradient-based control law, we prove local exponential stability with respect to the total energy by applying Chetaev's trick to the Lyapunov candidate function. We also propose a novel formation control law, which does not require measurements of relative positions but instead measurements of distances. The distance-only control law is based on an approximation of symmetric products of vector fields by sinusoidal perturbations. A suitable averaging analysis reveals that the averaged system coincides with the multi-agent system under the standard gradient-based control law. This allows us to prove practical exponential stability for the system under the distance-only control law.</p>}},
  author       = {{Suttner, Raik and Sun, Zhiyong}},
  booktitle    = {{2019 IEEE 58th Conference on Decision and Control, CDC 2019}},
  isbn         = {{978-1-7281-1399-9}},
  issn         = {{2576-2370}},
  language     = {{eng}},
  month        = {{03}},
  pages        = {{3521--3526}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{Proceedings of the IEEE Conference on Decision and Control}},
  title        = {{Exponential and practical exponential stability of second-order formation control systems}},
  url          = {{http://dx.doi.org/10.1109/CDC40024.2019.9030064}},
  doi          = {{10.1109/CDC40024.2019.9030064}},
  volume       = {{2019-December}},
  year         = {{2020}},
}