G. Lafferriere and A. Williams were supported in part by a grant from Honeywell, Inc. G. Lafferriere was supported in part by NSF Grant DMS-0408334 and by a Career Support grant from Portland State University.
Control theory -- Mathematical models, Multiagent systems -- Stability, Feedback control systems, Laplacian matrices
This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified communication digraph, G. A feedback control is designed using relative information between a vehicle and its in-neighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including symmetric communication graphs and formations with leaders. Several numerical simulations are used to illustrate the results.
Lafferriere, Gerardo; Williams, Anca; Caughman, John S. IV; and Veerman, J. J. P., "Decentralized Control of Vehicle Formations" (2004). Mathematics and Statistics Faculty Publications and Presentations. 142.