A lifting method for analyzing distributed synchronization on the unit sphere
(2018) In Automatica 96. p.253-258- Abstract
This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results... (More)
This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence.
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- author
- Thunberg, Johan LU ; Markdahl, Johan ; Bernard, Florian and Goncalves, Jorge
- publishing date
- 2018-10
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Asymptotic stabilization, Attitude synchronization, Consensus on the sphere, Control of constrained systems, Control of networks, Multi-agent systems
- in
- Automatica
- volume
- 96
- pages
- 6 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85050135190
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2018.07.007
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2018 Elsevier Ltd
- id
- 7cd044d2-f395-4b31-9079-920e15133b52
- date added to LUP
- 2024-09-05 12:29:35
- date last changed
- 2025-04-04 14:32:08
@article{7cd044d2-f395-4b31-9079-920e15133b52,
abstract = {{<p>This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence.</p>}},
author = {{Thunberg, Johan and Markdahl, Johan and Bernard, Florian and Goncalves, Jorge}},
issn = {{0005-1098}},
keywords = {{Asymptotic stabilization; Attitude synchronization; Consensus on the sphere; Control of constrained systems; Control of networks; Multi-agent systems}},
language = {{eng}},
pages = {{253--258}},
publisher = {{Elsevier}},
series = {{Automatica}},
title = {{A lifting method for analyzing distributed synchronization on the unit sphere}},
url = {{http://dx.doi.org/10.1016/j.automatica.2018.07.007}},
doi = {{10.1016/j.automatica.2018.07.007}},
volume = {{96}},
year = {{2018}},
}