Adaptive and Model Based Control Theory Applied to Convectively Unstable Flows

Abstract

Research on active control for the delay of laminar–turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review modelbased techniques, such as linearquadratic regulators, and modelfree adaptive methods, such as leastmean square filters. The former are supported by an elegant and powerful theoretical basis, whereas the latter may provide a more practical approach in the presence of complex disturbance environments that are difficult to model. We compare the methods with a particular focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the onedimensional linearized Kuramoto–Sivashinsky equation, which shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples is provided.