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Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle
KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.ORCID-id: 0000-0001-9940-5929
2014 (engelsk)Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, nr 7, s. 1722-1736Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that pi/4 is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

sted, utgiver, år, opplag, sider
2014. Vol. 59, nr 7, s. 1722-1736
Emneord [en]
Approximate projection, intersection computation, multi-agent systems, optimal consensus
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-148356DOI: 10.1109/TAC.2014.2309261ISI: 000338353300003Scopus ID: 2-s2.0-84903287276OAI: oai:DiVA.org:kth-148356DiVA, id: diva2:736523
Forskningsfinansiär
Knut and Alice Wallenberg FoundationSwedish Research Council
Merknad

QC 20140807

Tilgjengelig fra: 2014-08-07 Laget: 2014-08-05 Sist oppdatert: 2017-12-05bibliografisk kontrollert

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