# Events

Portland State University

Fariborz Maseeh Department of Mathematics & Statistics

The Maseeh Mathematics and Statistics Colloquium Series

Presents

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.