Speaker
Description
We develop and present a range of feedback control laws for the fluidic pinball control problem. This control problem seeks to control the vortex shedding behind three cylinders where cylinder rotation is the actuation mechanism. This benchmark problem has been used to demonstrate several machine learning control strategies. In this talk, we present an approach that uses interpolatory model reduction to build a polynomial approximation to the perturbation of the Navier-Stokes flow from the steady-state solution that maps the three control inputs to twenty-four output measurements taken downstream of the cylinders. Using this model, we use polynomial approximations to Hamilton-Jacobi-Bellman equations to create a quadratic feedback control law. Numerical simulations of this feedback law (a closed-loop simulation performed using FEniCS) demonstrate that we can completely stabilize the steady-state solution (i.e. no vortex shedding) over a range of low Reynolds number flows. We will comment on the sensitivity of the controller to boundary conditions.
