Article (Scientific journals)
Distributed methods for synchronization of orthogonal matrices over graphs
Thunberg, Johan; Bernard, Florian; Goncalves, Jorge
2017In Automatica, 80, p. 243–252
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Keywords :
Multi-agent systems; Distributed optimization; Sensor networks
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Thunberg, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Bernard, Florian ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
no
Language :
English
Title :
Distributed methods for synchronization of orthogonal matrices over graphs
Publication date :
June 2017
Journal title :
Automatica
ISSN :
0005-1098
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Volume :
80
Pages :
243–252
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
FnR Project :
FNR8864515 - Set Convergence In Nonlinear Multi-agent Systems, 2014 (01/02/2015-31/01/2017) - Johan Thunberg
Funders :
FNR - Fonds National de la Recherche [LU]
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