MIT Electrical Engineering and Computer Science EECS Event

Ergodic Theory and Control of Mixing

Prof. Igor Mezic
Harvard University

Tuesday, October 31, 2000
4:00 PM (reception following)
Room 35-225
LIDS Colloquium

Abstract

In this talk I will present some elements of the theory of control of mixing. It is, in fact, the control theory of measure-preserving systems with specific objectives, typically coming from ergodic theoretic considerations. The mixing objectives such as partition and Kolmogorov-Sinai entropy will be considered and a simple prototypical example of optimal control solved. Another possible objective is maximization of flux between different regions of fluid domain. A prototypical example in which this objective is used will be presented. It involves reduced-order modeling using vortex elements. Some results on controllability of vortex systems will be shown using flat coordinates. Finally, a contrast will be made between these results on controllability and a new concept of controllability via ergodicity.