Einladung zum Vortrag im Kolloquium Technische Kybernetik

Nonlinear Oscillations and the Steady-state Behavior for Nonlinear Feedback Systems

Prof. Christopher I. Byrnes
School of Engineering and Applied Science
Washington University · St. Louis · Missouri · USA

    Zeit: Dienstag,  05.05.2009 · 16:00 Uhr
    Ort: Seminarraum IST 3.243 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

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 field 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 sufficient 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 θ in polar coordinates is multi-valued. Conversely, using the recent solution of the Poincare Conjecture and related results, we show these sufficient conditions are necessary for the existence of an asymptotically stable oscillation.

Biographical Information

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 elected a Foreign Member of the Royal Swedish Academy of Engineering Sciences. A Fellow of the IEEE, with his coauthors he has (twice) received the IEEE George Axelby Award for best paper in the IEEE Trans. in Aut. Control and an IFAC Best Paper Award. He was awarded the SIAM Reid Prize in 2005 and the IEEE Hendrik W. Bode Prize in 2008. He is the Giovanni Prodi Chair in Nonlinear Analysis at the University of Wuerzburg for the Summer Semester 2009 and will spend the next academic year as Gast Professor at KTH.