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A lifting method for analyzing distributed synchronization on the unit sphere
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.ORCID iD: 0000-0002-9738-4148
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
Max-Planck-Institute for Informatics, Saarland Informatics Campus, Germany.
Systems Biomedicine, University of Luxembourg, Luxembourg.
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 96, p. 253-258Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Oxford: Pergamon Press, 2018. Vol. 96, p. 253-258
National Category
Other Mathematics Control Engineering
Identifiers
URN: urn:nbn:se:hh:diva-39452DOI: 10.1016/j.automatica.2018.07.007ISI: 000444659500026OAI: oai:DiVA.org:hh-39452DiVA, id: diva2:1317375
Available from: 2019-05-22 Created: 2019-05-22 Last updated: 2019-05-24Bibliographically approved

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Publisher's full texthttps://doi.org/10.1016/j.automatica.2018.07.007

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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