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Almost Global Consensus on the n-Sphere

Markdahl, Johan ; Thunberg, Johan LU and Goncalves, Jorge (2018) In IEEE Transactions on Automatic Control 63(6). p.1664-1675
Abstract

This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all \in \mathbb{N} \backslash \lbrace 1\rbrace$, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the nsphere for $n\in \mathbb{N}\backslash \lbrace 1\rbrace differs from the circle and \mathsf {SO}(3), where the... (More)

This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all \in \mathbb{N} \backslash \lbrace 1\rbrace$, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the nsphere for $n\in \mathbb{N}\backslash \lbrace 1\rbrace differs from the circle and \mathsf {SO}(3), where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on \mathsf {SO}(3) by combining two almost globally convergent protocols on the n-sphere for n\in \lbrace 1,2\rbrace. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on \mathsf {SO}(3).

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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Aerospace, agents and autonomous systems, consensus, cooperative control, nonlinear systems
in
IEEE Transactions on Automatic Control
volume
63
issue
6
pages
12 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85030635146
ISSN
0018-9286
DOI
10.1109/TAC.2017.2752799
language
English
LU publication?
no
additional info
Publisher Copyright: © 1963-2012 IEEE.
id
93469daa-2ede-45a7-992e-70b8011063a6
date added to LUP
2024-09-05 12:31:27
date last changed
2024-09-17 12:38:15
@article{93469daa-2ede-45a7-992e-70b8011063a6,
  abstract     = {{<p>This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all \in \mathbb{N} \backslash \lbrace 1\rbrace$, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the nsphere for $n\in \mathbb{N}\backslash \lbrace 1\rbrace differs from the circle and \mathsf {SO}(3), where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on \mathsf {SO}(3) by combining two almost globally convergent protocols on the n-sphere for n\in \lbrace 1,2\rbrace. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on \mathsf {SO}(3).</p>}},
  author       = {{Markdahl, Johan and Thunberg, Johan and Goncalves, Jorge}},
  issn         = {{0018-9286}},
  keywords     = {{Aerospace; agents and autonomous systems; consensus; cooperative control; nonlinear systems}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{1664--1675}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{Almost Global Consensus on the n-Sphere}},
  url          = {{http://dx.doi.org/10.1109/TAC.2017.2752799}},
  doi          = {{10.1109/TAC.2017.2752799}},
  volume       = {{63}},
  year         = {{2018}},
}