Robust reduced-order controller of laminar boundary layer transitions

A framework to derive optimal and robust reduced-order controllers of fluid mechanics and plasma physics flows using linear-quadratic-Gaussian design, or, in modern terms, ${\mathcal{H}}_{2}$ design, is presented. As a test case, two-dimensional channel flow is considered. A reduced model is derived, and a controller is designed based upon this model. Initial conditions creating transient growth of wall-shear stress are constructed. The controller is tested on a 32 wave number simulation. A wall-shear stress reduction, up to 90%, is obtained. The potential transferability of the controller to engineering applications is discussed.