ECE seminar series: From Linear Systems of Equations to Linear Dynamical Systems: A Talk on Distributed Controllers Design and Applications
Friday, May 17, 2013 – ( 1:30 pm to 2:30 pm )
Location: Babbio Center, Room 319
From Linear Systems of Equations to Linear Dynamical Systems: A Talk on Distributed Controllers Design and Applications
Consider that a linear time-invariant (LTI) plant is given and that we wish to design a stabilizing controller for it. As a general hypothesis throughout the talk, the controllers we are interested in - have access only to partial measurements. In the first part of the talk, as a way to model this hypothesis we impose that the class of admissible controllers (are LTI and) must comply with a pre-selected sparsity pattern. The sparsity pattern is assumed to be quadratically invariant (QI) with respect to the plant [Rotkowitz and Lall, 2006], which, from prior results, guarantees that there is a convex parameterization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. We address the previously unsolved problem of determining necessary and sufficient conditions for the existence of an admissible stabilizing controller. Our method also leads to a convex parameterization that may be viewed as an extension of Youla's classical approach so as to incorporate sparsity constraints. Applications of this parameterization on the design of norm-optimal controllers via convex methods are also discussed. In the second part of the talk we are interested in designing stabilizing (LTI) controllers that can be implemented over a communication network. We achieve this by exploring the Signal Structure and the subsequent Dynamical Structure Functions [as introduced by Goncalves and Warnick, 2008] of the admissible controllers. Numerically computational considerations are thoroughly provided for each of the proposed controller design algorithms.
Serban Sabau received his BA in Control Engineering from ``Politehnica'' University Bucharest, Romania in 2002 and his Ph.D. degree in Electrical Engineering from University of Maryland at College Park, in 2011. Since then he is a post-doctoral fellow at the University of Pennsylvania. His main research interests lie in the fields of distributed optimization, decentralized control, communication schemes with feedback and numerical linear algebra.