EVENT DETAILS AND ABSTRACT

Title: Symmetry in Chaos Control and Phase Space Reconstruction
Speaker: Dr. R. Grigoriev
Speaker Info: U. Chicago
Brief Description:
Special Note:
Abstract:

Active chaos control is believed to be an effective tool in suppressing undesired instabilities in turbine engine compressors, wide-aperture semiconductor lasers, and homoepitaxial surface growth. Unfortunately, conventional single-parameter chaos control techniques fail when applied to these complex systems. Upon closer examination we find that even such simple systems as an inverted pendulum in 2D or a system of two coupled oscillators with identical (or close) parameters present similar obstacles for control. Finally, it can be shown that phase space reconstruction cannot be performed for any of the above systems using the time delay embedding constructed from a sequence of measurements of its scalar output. I will show that all these problems result from neglecting the effects of intrinsic symmetries on the dynamics, specifically the degeneracy of the evolution operators. I will also show how the feedback control and the phase space reconstruction should be modified in the! presence of symmetry.