Finite-Time Weighted Average Consensus and Generalized Consensus Over a Subset

Shang, Yilun (2016) Finite-Time Weighted Average Consensus and Generalized Consensus Over a Subset. IEEE Access, 4. pp. 2615-2620. ISSN 2169-3536

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Official URL: http://dx.doi.org/10.1109/ACCESS.2016.2570518

Abstract

In this paper, the finite-time consensus for arbitrary undirected graphs is discussed. We develop a parametric distributed algorithm as a function of a linear operator defined on the underlying graph and provide a necessary and sufficient condition guaranteeing weighted average consensus in K steps, where K is the number of distinct eigenvalues of the underlying operator. Based on the novel framework of generalized consensus meaning that consensus is reached only by a subset of nodes, we show that the finite-time weighted average consensus can always be reached by a subset corresponding to the non-zero variables of the eigenvector associated with a simple eigenvalue of the operator. It is interesting that the final consensus state is shown to be freely adjustable if a smaller subset of consensus is admitted. Numerical examples, including synthetic and real-world networks, are presented to illustrate the theoretical results. Our approach is inspired by the recent method of successive nulling of eigenvalues by Safavi and Khan.

Item Type: Article
Uncontrolled Keywords: Weighted average consensus, generalized consensus, finite-time, discrete-time, distributed algorithm
Subjects: G100 Mathematics
G400 Computer Science
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Paul Burns
Date Deposited: 08 Nov 2018 14:05
Last Modified: 11 Oct 2019 18:04
URI: http://nrl.northumbria.ac.uk/id/eprint/36564

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