Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets
2013 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 3, 610-622 p.Article in journal (Refereed) Published
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, 610-622 p.
Connectivity Conditions, Distributed optimization, Intersection computation, Multi-agent systems, Optimal consensus
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-111438DOI: 10.1109/TAC.2012.2215261ISI: 000316806400005ScopusID: 2-s2.0-84874614056OAI: oai:DiVA.org:kth-111438DiVA: diva2:586288
FunderKnut and Alice Wallenberg FoundationSwedish Research Council
QC 201305082013-02-192013-01-112013-05-08Bibliographically approved