An Information Theoretic Viewpoint
to Performance Bounds of Feedback Systems: Optimality Results and Open Problems
Professor Nuno C. Martins
University
of Maryland – College Park
Department
of Electrical and Computer Engineering
In this seminar, I will discuss recent results on
universal bounds of performance
for feedback systems. By using
notions, from Information Theory, such as mutual information and
(differential) entropy, I characterize conservation laws that hold under
causality, which is a basic attribute of physical systems. In particular, I show that the
differential entropy, induced by external excitation, cannot be reduced by
feedback. This principle is related to the Bode integral formula, originally
derived for linear and time-invariant feedback systems. The aforementioned
analysis extends BodeÕs ideas to arbitrary feedback, while providing a suitable
framework for considering the case where a finite-horizon preview, of the
external excitation, is available. In addition, I will describe an information
flow inequality that can be used for establishing a universal bound of
performance, in the frequency domain. These results are expressed as bounds,
which, holding in great generality, are useful in establishing the optimality
of certain feedback schemes.
Bio: Nuno C Martins received the Licenciatura and the MS.
degrees in electrical engineering from Instituto Superior Tecnico, Lisbon,
Portugal in 1997 and the Ph.D. degree in electrical engineering and computer
science from Massachusetts Institute of Technology (MIT), Cambridge, in 2004.
In 2004 he was a Postdoctoral Associate at the Laboratory for Information and
Decision Systems, MIT. Currently, he is Assistant Professor at the Department
of Electrical and Computer Engineering, University of Maryland, College Park.
He is also affiliated with the Institute for Systems Research and his research
interests include fundamental limits of feedback and the fusion between control
theory and information theory.
Friday, April 7, 2006
3:30 – 4:30 p.m.
1500 EECS