Reference : A lifting method for analyzing distributed synchronization on the unit sphere
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/36099
A lifting method for analyzing distributed synchronization on the unit sphere
English
Thunberg, Johan mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Markdahl, Johan mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Bernard, Florian mailto [Saarland Informatics Campus > Max-Planck-Institute for Informatics]
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
2018
Automatica
Pergamon Press - An Imprint of Elsevier Science
Yes (verified by ORBilu)
International
0005-1098
Oxford
United Kingdom
[en] multi-agent systems ; consensus on the sphere ; attitude synchronization ; control of networks ; control of constrained systems ; asymptotic stabilization
[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.
Luxembourg Centre for Systems Biomedicine (LCSB)
Fonds National de la Recherche - FnR
Researchers ; Professionals
http://hdl.handle.net/10993/36099
FnR ; FNR8231540 > Jorge Gonçalves > GeDES > Genome-wide dynamical modelling differentially-regulated systems with application to the human T cell response > 01/09/2015 > 31/08/2018 > 2014

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