Modulus consensus in discrete-time signed networks and properties of special recurrent inequalities

Anton V. Proskurnikov, Ming Cao

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

11 Citations (Scopus)
36 Downloads (Pure)

Abstract

Recently the dynamics of signed networks, where the ties among the agents can be both positive (attractive) or negative (repulsive) have attracted substantial attention of the research community. Examples of such networks are models of opinion dynamics over signed graphs. It has been shown that under mild connectivity assumptions these protocols provide the convergence of opinions in absolute value, whereas their signs may differ. This 'modulus consensus' may correspond to the bipartite consensus (the opinions split into two clusters, converging to two opposite values) or the asymptotic stability of the system (the opinions always converge to zero). In this paper, we demonstrate that the phenomenon of modulus consensus in a signed network is a manifestation of a more general, regarding the solutions of special recurrent inequalities, associated to conventional first-order consensus algorithms. Although such a recurrent inequality does not provide the uniqueness of a solution, it can be shown that, under some natural assumptions, each of its bounded solutions has a limit and, moreover, converges to consensus. A similar property has previously been established for special continuous-time differential inequalities in [1]. Besides analysis of signed networks, we link the consensus properties of recurrent inequalities to the convergence properties of distributed optimization algorithms and stability properties of substochastic matrices.

Original languageEnglish
Title of host publicationProceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
EditorsA Astolfi et al
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Pages2003-2008
ISBN (Electronic)978-150902873-3
DOIs
Publication statusPublished - 2017
EventCDC 2017: 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017
http://cdc2017.ieeecss.org/

Conference

ConferenceCDC 2017: 56th IEEE Annual Conference on Decision and Control
CountryAustralia
CityMelbourne
Period12/12/1715/12/17
OtherThe CDC is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control. The CDC annually brings together an international community of researchers and practitioners in the field of automatic control to discuss new research results, perspectives on future developments, and innovative applications relevant to decision making, systems and control, and related areas.
Internet address

Bibliographical note

Accepted Author Manuscript

Fingerprint

Dive into the research topics of 'Modulus consensus in discrete-time signed networks and properties of special recurrent inequalities'. Together they form a unique fingerprint.

Cite this