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Stability and Robustness Issues in Decentralized Formation Control
Friday, February 19, 2010 - 3:15pm

Portland State University
Fariborz Maseeh Department of Mathematics & Statistics

The Maseeh Mathematics and Statistics Colloquium Series

Prabir Barooah, Ph.D.
~ Departmenmt of Mechanical and Aerospace Engineering, University of Florida~

Stability and Robustness Issues in Decentralized Formation Control

Formation control typically refers to the design of feedback control laws to move a group of agents along a given trajectory while maintaining a desired formation geometry. Each agent's control depends on the state of other vehicle. It has been known for some time that the coupled system exhibits poor stability margin and high sensitivity to external disturbances when the number of agents is large. Scalability becomes poorer when the control law is required to be decentralized, that is, when each agent is allowed to access information only from a small number of nearby agents to compute its control action. The difficulty in the decentralized formation control problem comes from several sources, one being the lack of appropriate control design and analysis tools. Classical control theory is useful to design only centralized control laws. In this talk we will discuss some recent developments on the analysis and design fronts for the formation control problem. The first part of the talk will describe application of graph-theoretic concepts to analyze the behavior of the system as a function of the number of agents and the topology of the interconnection network. The spectrum of the Dirichlet Laplacian matrix of the interconnection graph is seen to play a major role, which is then utilized to establish how performance scales with size and structure of the network. The second part of the talk is about a novel design methodology called "mistuning", which is suggested by a PDE approximation of the formation dynamics. The advantage of the PDE formulation is that it reveals the mechanism for loss of performance and ways to ameliorate much more clearly than the traditional state-space formulation does. The resulting mistuning design yields large improvement in the stability margin and robustness to disturbances compared to the traditional designs.

Friday, February 19th, 2010 at 3:15pm
Neuberger Hall Room 381
(Refreshments served at 3:00 in Neuberger Hall 344)

This event is free and open to the public.