A notion of generalized graph Laplacian and its application to distributed consensus algorithm

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

Original languageEnglish
Title of host publication2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program
Pages529-533
Number of pages5
Publication statusPublished - 2011
Event2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Zhengzhou
Duration: 2011 Aug 112011 Aug 13

Other

Other2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011
CityZhengzhou
Period11/8/1111/8/13

Fingerprint

Parallel algorithms

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Mechanical Engineering

Cite this

Zhai, G. (2011). A notion of generalized graph Laplacian and its application to distributed consensus algorithm. In 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program (pp. 529-533). [6024950]

A notion of generalized graph Laplacian and its application to distributed consensus algorithm. / Zhai, Guisheng.

2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program. 2011. p. 529-533 6024950.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhai, G 2011, A notion of generalized graph Laplacian and its application to distributed consensus algorithm. in 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program., 6024950, pp. 529-533, 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011, Zhengzhou, 11/8/11.
Zhai G. A notion of generalized graph Laplacian and its application to distributed consensus algorithm. In 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program. 2011. p. 529-533. 6024950
Zhai, Guisheng. / A notion of generalized graph Laplacian and its application to distributed consensus algorithm. 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program. 2011. pp. 529-533
@inproceedings{20799ea3994e4ba1af13a08832053840,
title = "A notion of generalized graph Laplacian and its application to distributed consensus algorithm",
abstract = "In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.",
keywords = "adjacency weights, cooperative control, distributed consensus algorithm, generalized graph Laplacian, graph Laplacian",
author = "Guisheng Zhai",
year = "2011",
language = "English",
isbn = "9780955529375",
pages = "529--533",
booktitle = "2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program",

}

TY - GEN

T1 - A notion of generalized graph Laplacian and its application to distributed consensus algorithm

AU - Zhai, Guisheng

PY - 2011

Y1 - 2011

N2 - In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

AB - In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of graph Laplacian by extending the adjacency weights from positive scalars to positive definite matrices. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application example, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.

KW - adjacency weights

KW - cooperative control

KW - distributed consensus algorithm

KW - generalized graph Laplacian

KW - graph Laplacian

UR - http://www.scopus.com/inward/record.url?scp=80053604720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053604720&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780955529375

SP - 529

EP - 533

BT - 2011 International Conference on Advanced Mechatronic Systems, ICAMechS 2011 - Final Program

ER -