Vortex Models for Feedback Stabilization of Wake Flows

This paper reviews recent progress concerning development of point-vortex reduced-order models for feedback stabilization of the cylinder wake flow. First, we recall briefly some earlier results related to the design of linear feedback stabilization strategies based on the Föppl system. Then we present derivation of a higher-order Föppl system bas on solutions of the Euler equations which desingularize the original Föppl vortices. We argue that such higher-order Föppl systems possess important advantages over the classical Föppl system which are relevant from the control-theoretic point of view. In particular, we present computational results indicating that a higher-order Föppl system can be stabilized completely in contrast to the classical Föppl system for which this is not possible owing to the presence of a stable center manifold spanned by uncontrollable modes.