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Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2013 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 3, p. 610-622Article in journal (Refereed) Published
Abstract [en]

In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuoustime algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis.

Place, publisher, year, edition, pages
IEEE Press, 2013. Vol. 58, no 3, p. 610-622
Keyword [en]
Connectivity Conditions, Distributed optimization, Intersection computation, Multi-agent systems, Optimal consensus
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-111438DOI: 10.1109/TAC.2012.2215261ISI: 000316806400005Scopus ID: 2-s2.0-84874614056OAI: oai:DiVA.org:kth-111438DiVA: diva2:586288
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20130508

Available from: 2013-02-19 Created: 2013-01-11 Last updated: 2017-12-06Bibliographically approved

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Johansson, Karl Henrik

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