University of Minnesota
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Electrical and Computer Engineering

Design of Optimal Stuctured Controllers for Large-scale Interconnected Systems

Mihailo Jovanovic
University of Minnesota

We consider the design of optimal static feedback gains for interconnected systems subject to structural
constraints on the distributed controller. These constraints are in the form of sparsity requirements for the
feedback matrix, implying that each controller has access to information from only a limited number of
subsystems. For this non-convex constrained optimal control problem, we derive necessary conditions
for optimality in the form of coupled matrix equations. For stable open-loop systems, we show that in the
limit of expensive control, the optimal controller can be found analytically using perturbation techniques.
We use this feedback gain to initialize homotopy-based Newton iteration that finds an optimal solution
to the original (non-expensive) control problem. We further employ the augmented Lagrangian method to
alleviate the difficulty of finding a stabilizing structured gain to initialize efficient Newton and quasi-Newton
methods that exploit the sparsity structure of the constraint set. The developed technique is used to design
optimal localized controllers in large-scale vehicular formations. The issue of scaling, with respect to the
number of vehicles, of global and local performance measures in the optimally-controlled formation will be
discussed in detail.

Mihailo Jovanovic received the Dipl. Ing. and M.S. degrees from the University of Belgrade, Serbia, in 1995
and 1998, respectively, and the Ph.D. degree from the University of California, Santa Barbara, in 2004.
He was a Visiting Researcher with the Department of Mechanics, the Royal Institute of Technology,
Stockholm, Sweden, from September to December 2004. He joined the University of Minnesota,
Minneapolis, as an Assistant Professor of Electrical and Computer Engineering in December 2004.
His primary research interests are in modeling, analysis, and control of spatially distributed dynamical
systems. He is a member of IEEE, SIAM, and APS and an Associate Editor of the IEEE Control Systems
Society Conference Editorial Board. He received a CAREER Award from the National Science Foundation
in 2007.