Optimal feedback control of the incompressible Navier-Stokes-Equations using reduced order models

A novel scheme for an optimal feedback-control of distributed parameter systems is proposed. Therefore, the optimal control problem for the two-dimensional incompressible Navier-Stokes-Equations with an actuation via boundary-conditions is set up. Afterwards the Navier-Stokes-Equations and their adjoint equations are solved numerically. A model reduction is performed for both solutions using the POD-Galerkin procedure. The optimal feedback control is computed online from the reduced order models in each time step without need of further optimization. Results are shown for closed-loop simulations with the Navier-Stokes-Equations.