Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

Linear and Nonlinear Prediction, Filtering and Control of Dynamical Systems

by Kenneth Showalter
Department of Chemistry
West Virginia University
Morgantown, WV 26506-6045

MIDIT-seminar No. 404

Wednesday, April 15, 14:00 h
at MIDIT, IMM Building 305, room 027

Abstract Feedback methods for stabilizing unstable states will be described and applications to chemical systems will be presented. Controlling states with more than one unstable direction remains an important challenge. Such states are common in spatially extended systems, and techniques beyond those developed for low-dimensional systems are required for controlling spatiotemporal chaos. A method for stabilizing and characterizing states with many unstable degrees of freedom will be described. This method provides an explicit connection between phase-space approaches and the linear control routines of classical single-input, single-output systems. Nonlinear prediction, filtering and control is carried out by using time series to create an invariant hypersurface in the delayed state space. This can be used to drive a system to any particular objective state or to extract low-dimensional deterministic signals such as the time series of one observable from the time series of the another.