NDLI: Distributed Matrix Scaling and Application to Average Consensus in Directed Graphs

Content Provider	IEEE Xplore Digital Library
Author	Dominguez-Garcia, A.D. Hadjicostis, C.N.
Copyright Year	1963
Abstract	We propose a class of distributed iterative algorithms that enable the asymptotic scaling of a primitive column stochastic matrix, with a given sparsity structure, to a doubly stochastic form. We also demonstrate the application of these algorithms to the average consensus problem in networked multi-component systems. More specifically, we consider a setting where each node is in charge of assigning weights on its outgoing edges based on the weights on its incoming edges. We establish that, as long as the (generally directed) graph that describes the communication links between components is strongly connected, each of the proposed matrix scaling algorithms allows the system components to asymptotically assign, in a distributed fashion, weights that comprise a primitive doubly stochastic matrix. We also show that the nodes can asymptotically reach average consensus by executing a linear iteration that uses the time-varying weights (as they result at the end of each iteration of the chosen matrix scaling algorithm).
Sponsorship	IEEE Control Systems Society
Starting Page	667
Ending Page	681
Page Count	15
File Size	4733070
File Format	PDF
ISSN	00189286
Volume Number	58
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Convergence Algorithm design and analysis Terrorism Distributed algorithms Vectors Topology nonnegative matrix Average consensus directed graph distributed algorithms matrix scaling
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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