Creator:

Zhai, Guisheng

Contributor:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Title:

A generalization of the graph Laplacian with application to a distributed consensus algorithm

Group publication title:

AMCS, Volume 25 (2015)

Subject and Keywords:

graph Laplacian ; generalized graph Laplacian ; adjacency weights ; distributed consensus algorithm ; cooperative control

Abstract:

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Resource Type:

artykuł

DOI:

10.1515/amcs-2015-0027

Pages:

353-360

Source:

AMCS, volume 25, number 2 (2015) ; click here to follow the link

Language:

eng

Rights:

Biblioteka Uniwersytetu Zielonogórskiego