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Multiequilibria analysis for a class of collective decision-making networked systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-6367-6302
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-4142-6502
2018 (English)In: IEEE Transactions on Control of Network Systems, E-ISSN 2325-5870, no 4, p. 1931-1940Article in journal (Refereed) Published
Abstract [en]

The models of collective decision-making considered in this paper are nonlinear interconnected cooperative systems with saturating interactions. These systems encode the possible outcomes of a decision process into different steady states of the dynamics. In particular, they are characterized by two main attractors in the positive and negative orthant, representing two choices of agreement among the agents, associated to the Perron-Frobenius eigenvector of the system. In this paper we give conditions for the appearance of other equilibria of mixed sign. The conditions are inspired by Perron-Frobenius theory and are related to the algebraic connectivity of the network. We also show how all these equilibria must be contained in a solid disk of radius given by the norm of the equilibrium point which is located in the positive orthant.

Place, publisher, year, edition, pages
2018. no 4, p. 1931-1940
Keywords [en]
Symmetric matrices;Eigenvalues and eigenfunctions;Bifurcation;Neural networks;Decision making;Control systems;Cooperative systems;Collective decision-making;nonlinear cooperative systems;multiple equilibria;Perron-Frobenius theorem;algebraic connectivity
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-151688DOI: 10.1109/TCNS.2017.2774014ISI: 000454245200038OAI: oai:DiVA.org:liu-151688DiVA, id: diva2:1252619
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-10-02 Created: 2018-10-02 Last updated: 2019-01-11

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Fontan, AngelaAltafini, Claudio

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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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