"IMPORTANT MOMENTS IN SYSTEMS AND CONTROL"
Christopher I. Byrnes
Department of Electrical and Computer Engineering
Washington University
St Louis, Missouri, USA
The moment problem as formulated by Krein and Nudel’man is a beautiful generalization
of several important classical moment problems, including the power moment problem,
the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick
interpolation. Motivated by classical applications and examples, in both finite and infinite
dimensions, we recently formulated a new version of this problem that we call the moment
problem for positive rational measures. The formulation reflects the importance of rational
functions in signals, systems and control, where there have been applications to circuit
theory, model reduction, time-optimal control, robust control, signal processing, spectral
estimation, stochastic realization theory and the use of the moments of a probability density.
While the rational version of the problem is decidedly nonlinear, the basic tools still
rely on convexity. In this talk, we present a solution to this problem that combines basic
analysis and topology in Euclidean space with a nonlinear convex optimization problem
that generalizes the maximum entropy approach used in several classical special cases.
Short biography:
Chris Byrnes has made fundamental contributions to the application of mathematics to
engineering, particularly to the areas of systems, signals and control. The author of about
250 technical papers and books, he and A. Isidori received the IEEE George Axelby Best
Paper Award for their work on output regulation for nonlinear control systems in 1991. In
1993, they shared the IFAC Automatica Best Paper Prize for a paper in which they solved
a longstanding problem on the control of a rigid body model of a satellite in an actuator
failure mode. In 2003, T. T. Georgiou, A. Lindquist and Chris shared the IEEE George
Axelby Best Paper Award for work applying these methods to Nevanlinna-Pick
interpolation. In 2005, he was awarded the Reid prize from SIAM for his contributions to
Control Theory and Differential Equations. He was named the 2008 Hendrik Bode Prize
Lecturer by the IEEE and will hold the Giovanni Prodi Chair in Nonlinear Analysis at the
University of Wuerzburg in 2009. He is a Fellow of the IEEE and a Foreign Member of
the Royal Swedish Academy of Engineering Sciences. His current interests include the
application of dynamics and topology to nonequilibrium problems in control, particularly
the behavior of periodic steady state response for nonlinear control systems.
(slides
http://homes.esat.kuleuven.be/%7Eoptec/events/20080509_byrnes.pdf )
