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Graph Laplacians and Stabilization of Vehicle Formations

Fax, J. Alexander and Murray, Richard M. (2001) Graph Laplacians and Stabilization of Vehicle Formations. California Institute of Technology . (Unpublished)

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Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies.

Item Type:Report or Paper (Technical Report)
Murray, Richard M.0000-0002-5785-7481
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2001.01-007
Persistent URL:
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28001
Deposited By: Imported from CaltechCDSTR
Deposited On:23 Sep 2002
Last Modified:03 Oct 2019 03:28

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