Vortex dynamics models in flow control problems

In this article we review the state of the art in the field of control of vortex dynamics. We focus on problems governed by two-dimensional incompressible Euler equations in domains both with and without boundaries. Following a comprehensive review of earlier approaches, we discuss how methods of modern control and optimization theory can be employed to solve control problems for vortex systems. In addition, we address the companion problem of the state estimation for vortex systems. While most of the discussion concerns point vortex systems, in the second part of the article we also introduce a novel approach to the control of Euler flows involving finite-area vorticity distributions. The article concludes with what, in the author's opinion, represent promising new research directions.