Distributed methods for synchronization of orthogonal matrices over graphs
(2017) In Automatica 80. p.243-252- Abstract
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization... (More)
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations.
(Less)
- author
- Thunberg, Johan LU ; Bernard, Florian and Goncalves, Jorge
- publishing date
- 2017-06-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Consensus algorithms, Distributed optimization, Measurement and instrumentation, Multi-agent systems, Robust estimation, Sensor networks
- in
- Automatica
- volume
- 80
- pages
- 10 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85016150108
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2017.02.025
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017 Elsevier Ltd
- id
- bad26aa2-1c9c-449f-9f96-3bd1d80fe2b1
- date added to LUP
- 2024-09-05 12:32:38
- date last changed
- 2025-04-04 15:03:32
@article{bad26aa2-1c9c-449f-9f96-3bd1d80fe2b1,
abstract = {{<p>This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations.</p>}},
author = {{Thunberg, Johan and Bernard, Florian and Goncalves, Jorge}},
issn = {{0005-1098}},
keywords = {{Consensus algorithms; Distributed optimization; Measurement and instrumentation; Multi-agent systems; Robust estimation; Sensor networks}},
language = {{eng}},
month = {{06}},
pages = {{243--252}},
publisher = {{Elsevier}},
series = {{Automatica}},
title = {{Distributed methods for synchronization of orthogonal matrices over graphs}},
url = {{http://dx.doi.org/10.1016/j.automatica.2017.02.025}},
doi = {{10.1016/j.automatica.2017.02.025}},
volume = {{80}},
year = {{2017}},
}