Title: Optimal Control of Vortex Systems

In this presentation we review the recent progress regarding application of modern optimal control theory to stabilization of hydrodynamic instabilities based on point vortex models. First we show how optimal feedback control methods arise as solutions of suitable optimization problems. We focus on the control of bluff body wake flows modeled by the Föppl point vortex system. It is demonstrated how such models can be stabilized using the Linear-Quadratic-Gaussian (LQG) optimal control approach. We prove the existence of a center manifold in the Föppl system with the feedback control and discuss how it affects the effectiveness of the control strategy. We also show how properties of such reduced-order models for flow control can be improved by constructing a family of higher-order Föppl systems. Results of our mathematical analysis will be illustrated with several computational examples. The presentation will conclude with some remarks concerning optimal control of Euler flows with finite-area vortex regions.