Convex Parameterizations for Norm-Optimal Linear Control


Event Speaker: 

Nuno Martins (Univ. of Maryland)

Event Location: 


Event Date/Time: 

Tuesday, November 20, 2012 - 4:00pm

Reception to follow.
In this talk I will cover new results, principles and methods for the design of norm optimal controllers subject to information constraints. The main problem will be motivated first for the LQG case using a classical team decision theoretic framework, and connections to the deterministic case will be explored. In particular, I will explain why structural invariance properties (such as Quadratic Invariance proposed by Rotkowitz and Lall) commonly used in the deterministic case also imply partial nestedness for the LQG case. This is important because partial nestedness is known to guarantee the existence of optimal solutions that are LTI. The second part of the talk focuses on the design of LTI norm-optimal controllers subject to a sparsity pattern that is assumed to be quadratically invariant (QI) with respect to the plant, which, from prior results, guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. I will present a solution to the previously unsolved problem of determining necessary and sufficient conditions for the existence of an admissible stabilizing controller. The main idea is to cast the existence of such a controller as the feasibility of an exact model-matching problem with stability restrictions, which can be tackled using existing methods. Furthermore, I will show that, when it exists, the solution of the model-matching problem can be used to compute an admissible stabilizing controller. This method also leads to a convex parametrization that may be viewed as an extension of Youla’s classical approach so as to incorporate sparsity constraints. Applications of this parametrization on the design of norm-optimal controllers via convex methods are also explored. An illustrative example is provided, and a special case is discussed for which the exact model matching problem has a unique and easily computable solution. This work was developed in collaboration with Dr. Serban Sabau.
Nuno C. Martins received the MS. degree in electrical engineering from I.S.T., Portugal, in 1997, and the Ph.D. degree in Electrical Engineering and Computer Science with a minor in Mathematics from Massachusetts Institute of Technology (MIT), Cambridge, in 2004. He has also concluded a Financial Technology Option program at Sloan School of Management (MIT) in 2004. He is currently Associate Professor at the Department of Electrical and Computer Engineering, University of Maryland, College Park, where he is also affiliated with the Institute for Systems Research and the Maryland Robotics Center for which he serves as director. He received a National Science Foundation CAREER award in 2007, the 2006 American Automatic Control Council O. Hugo Schuck Award, the 2010 Outstanding ISR Faculty award, the 2010 IEEE CSS Axelby Award and a 2012-13 University of Maryland Leadership Fellowship. He is also a member of the editorial board of Systems and Control Letters (Elsevier), Automatica and of the IEEE Control Systems Society Conference Editorial Board.