Article (Scientific journals)
A lifting method for analyzing distributed synchronization on the unit sphere
THUNBERG, Johan; MARKDAHL, Johan; Bernard, Florian et al.
2018In Automatica
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Keywords :
multi-agent systems; consensus on the sphere; attitude synchronization; control of networks; control of constrained systems; asymptotic stabilization
Abstract :
[en] 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.
Research center :
Luxembourg Centre for Systems Biomedicine (LCSB)
Disciplines :
Mathematics
Author, co-author :
THUNBERG, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
MARKDAHL, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Bernard, Florian;  Saarland Informatics Campus > Max-Planck-Institute for Informatics
GONCALVES, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
yes
Language :
English
Title :
A lifting method for analyzing distributed synchronization on the unit sphere
Publication date :
2018
Journal title :
Automatica
ISSN :
0005-1098
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
FnR Project :
FNR8231540 - Genome-wide Dynamical Modelling Differentially-regulated Systems With Application To The Human T Cell Response, 2014 (01/09/2015-31/08/2018) - Jorge Gonçalves
Funders :
FNR - Fonds National de la Recherche [LU]
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since 08 July 2018

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