Computation of Decentralized Controllability for Large-Scale Systems

ECE Seminar: Computation of Decentralized Controllability for Large-Scale Systems


Starts at: April 5, 2018 4:30 PM

Ends at: 6:00 PM

Location: WEH 5421

Speaker: Dr. Michael Rotkowitz

Affiliation: University of Maryland

Refreshments provided: Yes

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Abstract
This talk will discuss the computation of non-binary measures of decentralized controllability and stabilizability.

We first review what fixed modes are and how they determine whether an LTI system is controllable or stabilizable with a decentralized LTI controller of given information structure. Just as with these notions for centralized control, they provide no information on robustness or the necessary control effort in the positive case. We then review work, that of Vaz and Davison from 1988 in particular, which studies how far a system is from having a fixed mode (and losing controllability/stabilizability).

This results in extremely difficult optimization problems, which could only be solved for very small instances, thus defeating the goal of applying them to large-scale complex systems. The two main difficulties which arise are a combinatorial component (where one must minimize over the power set of the subsystems), and the seemingly unstudied problem of minimizing a particular (neither the largest nor the smallest) singular value of a matrix variable. For the remainder of the talk, we discuss how we have addressed these difficulties to provide scalable upper and lower bounds for these metrics.

Addressing the combinatorial component led to work in MINLP, including an ADMM-based algorithm which shed light on the importance of choosing how to split variables for nonconvex ADMM. The singular value minimization led to a counterintuitive result for the best convex heuristic when seeking upper bounds, and led to the development of sampling techniques from the Courant-Fischer characterization when seeking lower bounds. (If there is sufficient interest, an additional talk can be given the following day focusing on the singular value minimization problem.)

This is joint work with Alborz Alavian.

Bio
Michael C. Rotkowitz received a B.S. in Mathematical and Computational Science, an M.S. in Statistics, and an M.S. and Ph.D. in Aeronautics and Astronautics, all from Stanford University.

He was a Postdoctoral Fellow at the Royal Institute of Technology (KTH) in Stockholm, Sweden from 2005-6, and a Research Fellow with the Australian National University in Canberra, Australia from 2006-8. From 2008-11 he served as a Research Fellow, Senior Research Fellow, and Queen Elizabeth II Fellow at the University of Melbourne. Since 2012 he has been Assistant Professor in the Department of Electrical and Computer Engineering (ECE) and the Institute for Systems Research (ISR) at the University of Maryland at College Park, where he is also affiliated with the Applied Mathematics & Statistics, and Scientific Computation Program (AMSC).

Prof. Rotkowitz has been the recipient of several awards including the 2007 IEEE George S. Axelby Outstanding Paper Award, the 2011 SIAM Control and Systems Theory Prize, a 2014 NSF CAREER Award, and the Presidential Early Career Award for Scientists and Engineers (PECASE).