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Persis en Flows in Deterministic Chains
Dalian Univ Technol, Sch Control Sci & Engn, Dalian 116023, Peoples R China..
Univ Sydney, Sch Aerosp Mech & Mechatron Engn, Australian Ctr Field Robot, Sydney, NSW 2008, Australia.;Australian Natl Univ, Res Sch Engin, Canberra, ACT 0200, Australia..
Tsinghua Univ, Dept Precis Instrument, State Key Lab Precis Measurement Technol & Instru, Beijing 100084, Peoples R China..
Univ Groningen, Engn & Technol Inst Groningen, Fac Sci & Engn, NL-9712 Groningen, Netherlands..
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2019 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 7, p. 2766-2781Article in journal (Refereed) Published
Abstract [en]

This paper studies, the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l(1) norm; convergence of the infinite backward products to a rank-one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states. We discuss two balance conditions on the interactions between agents, which generalize the arc-balance and cut-balance conditions in the literature, respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2019. Vol. 64, no 7, p. 2766-2781
Keywords [en]
Consensus, multiagent systems, persistent graphs, products of stochastic matrices
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-255430DOI: 10.1109/TAC.2019.2893974ISI: 000473489700009Scopus ID: 2-s2.0-85068126768OAI: oai:DiVA.org:kth-255430DiVA, id: diva2:1344194
Note

QC 20190820

Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2019-08-20Bibliographically approved

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Johansson, Karl H.

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