Stability and control of shear flows subject to stochastic excitations

Abstract: In this thesis, we adapt and apply methods from linear control theory to shear flows. The challenge of this task is to build a linear dynamic system that models the evolution of the flow, using the Navier--Stokes equations, then to define sensors and actuators, that can sense the flow state and affect its evolution. We consider flows exposed to stochastic excitations. This framework allows to account for complex sources of excitations, often present in engineering applications. Once the system is built, including dynamic model, sensors, actuators, and sources of excitations, we can use standard optimization techniques to derive a feedback law. We have used feedback control to stabilize unstable flows, and to reduce the energy level of sensitive flows subject to external excitations.