A generalization of the graph Laplacian with application to a distributed consensus algorithm
International Journal of Applied Mathematics and Computer Science (2015)
- Volume: 25, Issue: 2, page 353-360
- ISSN: 1641-876X
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topGuisheng Zhai. "A generalization of the graph Laplacian with application to a distributed consensus algorithm." International Journal of Applied Mathematics and Computer Science 25.2 (2015): 353-360. <http://eudml.org/doc/270629>.
@article{GuishengZhai2015,
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.},
author = {Guisheng Zhai},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {graph Laplacian; generalized graph Laplacian; adjacency weights; distributed consensus algorithm; cooperative control},
language = {eng},
number = {2},
pages = {353-360},
title = {A generalization of the graph Laplacian with application to a distributed consensus algorithm},
url = {http://eudml.org/doc/270629},
volume = {25},
year = {2015},
}
TY - JOUR
AU - Guisheng Zhai
TI - A generalization of the graph Laplacian with application to a distributed consensus algorithm
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 2
SP - 353
EP - 360
AB - 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.
LA - eng
KW - graph Laplacian; generalized graph Laplacian; adjacency weights; distributed consensus algorithm; cooperative control
UR - http://eudml.org/doc/270629
ER -
References
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