Learning Linear Feedback Controllers for Suppressing the Vortex-Shedding Flow Past a Cylinder

In this letter, we propose a method to learn linear time-invariant controllers that completely suppress the vortex-shedding regime past a cylinder at Reynolds number 100, using a single actuator and sensor pair in a feedback configuration. The method is based on the Youla parametrization for guaranteeing closed-loop stability in a neighbourhood of the fixed point. Among the set of controllers stabilizing the fixed point, a derivative-free optimization algorithm searches for a controller suppressing the natural limit cycle oscillation. We show existence of simple single input, single output, linear time-invariant controllers driving the full vortex shedding regime to the natural unstable base flow for large dimension, highly nonlinear Navier-Stokes dynamics.