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Dynamic controllers for column synchronization of rotation matrices: A QR-factorization approach
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).ORCID iD: 0000-0002-9738-4148
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, p. 20-25Article in journal (Refereed) Published
Abstract [en]

In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d−1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d−k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.

Place, publisher, year, edition, pages
Oxford: Pergamon Press, 2018. Vol. 93, p. 20-25
National Category
Control Engineering Other Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-39455DOI: 10.1016/j.automatica.2018.03.023ISI: 000436916200003OAI: oai:DiVA.org:hh-39455DiVA, id: diva2:1317397
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.2018.03.023

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
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  • vancouver
  • Other style
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  • 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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