Closed-Loop Control of Fluid Flow: a Review of Linear Approaches and Tools for the Stabilization of Transitional Flows

Flow control is concerned with the targeted manipulation of intrinsic flow behavior to optimally satisfy prescribed objectives. This article will give an overview of the most common tools for the design of control strategies. We focus on linear control that is aimed at stabilizing fixed points of the Navier-Stokes equations, such as those existing in the case of transitional flows. Key steps to build a Galerkin-based and a data-based model will be presented and illustrated on two generic flow configurations: flow over an open cavity and over a backward-facing step. In the former case, a feedback configuration will result and particular attention will be paid to performance measures and robustness analyses. For the latter case, a feedforward setup has been chosen and a system-identification method will be employed to extract the fluid behavior from data sequences, via statistical learning techniques.