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Finite state $\rho/ \mu$ approximations for control design

Hybrid systems, involving interacting continuous and discrete dynamics, are pervasive in both manmade and natural systems and pose a broad spectrum of technical challenges. While several frameworks have been investigated, the past decade has witnessed particular interest in finite state approximations as a means of attacking some of these technical challenges. In particular, plants that are constrained to interact with their controllers via fixed discrete alphabet sets ( `systems over finite alphabets' ) can be thought of as a special class of hybrid systems: Effectively, the discrete alphabet setting gives rise to non-trivial state estimation problems, in addition to the challenging control design problems inherent in hybrid dynamics.

In this talk, we survey a set of analysis tools that are tailored towards systems over finite alphabets, as well as synthesis tools for finite state models. A common component of these tools is the use of input/output constraints as a means of describing system properties of interest. We then propose a notion of approximation, referred to as '$\rho / \mu$ approximation', that seeks to approximate systems over finite alphabets by finite memory models, and to quantify the quality of approximation in a manner compatible with the developed analysis and synthesis tools. Finally, we present constructive algorithms for generating such $\rho/\mu$ approximations.

Type of Seminar:
IfA Seminar
Prof. Danielle C. Tarraf
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore
Jun 07, 2012   16:15

HG E 21, Rämistr. 101
Contact Person:

John Lygeros
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Biographical Sketch:
Danielle C. Tarraf is an Assistant Professor of Electrical and Computer Engineering at the Johns Hopkins University. She previously held postdoctoral positions in the Division of Control and Dynamical Systems at the California Institute of Technology (2007-2008) and in the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology (2006-2007). She received her B.E. degree from the American University of Beirut in 1996, and her M.S. and Ph.D. degrees from the Massachusetts Institute of Technology in 1998 and 2006, respectively.

Her research interests are in the broad area of systems and control theory, particularly as it interfaces with theoretical computer science. Her current focus includes control of hybrid systems; finite memory approximations for control design; problems at the interface of control, algebra, combinatorics, and automata theory; and analysis and robust control of networks.

Prof. Tarraf is the recipient of a 2010 CAREER award from the National Science Foundation, a 2011 Young Investigator Award from the Air Force Office of Scientific Research, and a 2012 Johns Hopkins University Alumni Excellence in Teaching award.