A numerical approach to the control and stabilization of advection-diffusion systems: Application to viscous drag reduction

In this article we investigate computational methods for the control and st abilization of systems modeled by parabolic equations of the advection-reac tion-diffusion type and by the Navier-Stokes equations for incompressible v iscous fluids. For the first class of control problems we shall discuss ope n loop control methods and closed loop methods a la Riccati. Concerning the second class of problems we shall consider the Dirichlet boundary control of flow around cylinders and attempt to reduce the viscous drag. The result s of numerical experiments will Validate the computational methods describe d in this article.