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

• Autorzy: Guisheng Zhai
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: 25
• Numer: 2
• Strony: 353-360

Daty

wydano

2015

otrzymano

2014-01-06

poprawiono

2014-07-07

Twórcy

autor

Guisheng Zhai

• Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan

Bibliografia

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Identyfikatory

DOI

10.1515/amcs-2015-0027