Kim Engineering Building, Rm. 1110
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301 405 3596
Booz Allen Hamilton Distinguished Colloquium in Electrical and Computer Engineering
"Nonlinear Oscillations and the Steady-state Behavior for Nonlinear Feedback Systems"
Dr. Christopher Byrnes
Edward H. and Florence G. Skinner Professor of Systems Science and Mathematics, Washington University, St. Louis
March 6, 2009, 2:00 p.m.
Jeong H. Kim Engineering Building, Rm. 1110
A long term goal in the theory of systems and control is to develop a systematic methodology for the design of feedback control schemes capable of shaping the response of complex dynamical systems, in both an equilibrium and a nonequilibrium setting. In this talk, we will focus primarily on periodic steady-state behavior, a phenomenon that is pervasive in nature and in man-made systems. As an example, we review how a rotation in a magnetic eld produces a stable nonlinear oscillation in a three dimensional, nonlinear model of an AC controlled rotor resulting in a constant steady-state angular velocity of the rotor. We will also show how to design feedback laws for stabilizable n-dimensional systems so that the existence, periods and stability of periodic responses can be analyzed and shaped when the nonlinear feedback system is driven with an arbitrary periodic input. This design is the result of joint work with joint work with R. Brockett and with A. Isidori. In particular, we will present sucient conditions for the existence of nonlinear oscillations in terms of a multi-valued analogue of Liapunov functions, in much the same way as the angular variable in polar coordinates is multi-valued. Conversely, using the recent solution of the Poincare Conjecture and related results, we show these sucient conditions are necessary for the existence of an asymptotically stable oscillation.
Chris Byrnes is the Edward H. and Florence G. Skinner Professor of Systems Science and Mathematics at Washington University in St. Louis. The author of more than 250 technical papers and books, Chris received an Honorary Doctorate of Technology from the Royal Institute of Technology (KTH) in Stockholm in 1998 and in 2002 was named a Foreign Member of the Royal Swedish Academy of Engineering Sciences. He is a Fellow of the IEEE, has twice received (with his coauthors) the IEEE George Axelby Award for best paper in the IEEE Trans. in Aut. Control and has also received the IFAC Best Paper Award. In 2005, he was awarded the Reid Prize from SIAM for ‘his contributions to control theory and differential equations”. In December 2008, he received the IEEE Hendrik W. Bode Prize and gave the Bode Prize Lecture at the annual IEEE Conference on Decision and Control. He will hold the Giovanni Prodi Chair in Nonlinear Analysis at the University of Wuerzburg in the Summer Semester of 2009 and spend the 2009-2010 academic year as Gast Professor at KTH, supported by the Swedish Strategic Research Foundation.
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