Graph weight design for Laplacian eigenvalue constraints with multi-agent systems applications

Author

Shafi, S. Yusef ; Arcak, Murat ; El Ghaoui, Laurent

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA

fYear

2011

fDate

12-15 Dec. 2011

Firstpage

5541

Lastpage

5546

Abstract

We adjust the node and edge weightings of graphs using convex optimization to impose bounds on their Laplacian spectra. We first derive necessary and sufficient conditions that characterize the feasibility of spectral bounds given positive node and edge weightings. Next, we propose algorithms that exploit convexity to achieve these bounds. The design and analysis tools are useful for a variety of stability and control problems in multi-agent systems.

Keywords

convex programming; eigenvalues and eigenfunctions; graph theory; multi-agent systems; multi-robot systems; Laplacian eigenvalue constraint; Laplacian spectra; convex optimization; edge weightin; graph weight design; multi-agent systems application; necessary condition; node weight; sufficient condition; Aircraft; Clustering algorithms; Eigenvalues and eigenfunctions; Laplace equations; Linear matrix inequalities; Multiagent systems; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Conference_Location

Orlando, FL

ISSN

0743-1546

Print_ISBN

978-1-61284-800-6

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2011.6160545

Filename

6160545