Distributed matrix scaling and application to average consensus in directed graphs
Date
2013Source
IEEE Transactions on Automatic ControlVolume
58Issue
3Pages
667681Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
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 multicomponent 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 timevarying weights (as they result at the end of each iteration of the chosen matrix scaling algorithm). © 19632012 IEEE.
Collections
Cite as
Related items
Showing items related by title, author, creator and subject.

Conference Object
A neuraltype parallel algorithm for fast matrix inversion
Polycarpou, Marios M.; Ioannou, P. A. (1991)

Conference Object
Exact filters for NewtonRaphson parameter estimation algorithms for continuoustime partially observed stochastic systems
Charalambous, Charalambos D.; Logothetis, Andrew; Hibey, Joseph L. (IEEE, 1999)This paper presents explicit finitedimensional filters for implementing NewtonRaphson (NR) parameter estimation algorithms. The models which exhibit nonlinear parameter dependence are stochastic, continuoustime and ...

Conference Object
A convex programming approach to the multiobjective H2/H∞ problem
Djouadi, S. M.; Charalambous, Charalambos D.; Repperger, D. W. (2002)In this paper, Banach space duality theory for the multiobjective H2/H∞ problem developed recently by the authors, is used to develop algorithms to solve this problem by approximately reducing the dual and predual ...