Optimal control of fluid-structure interaction systems : the case of a rigid solid

This report deals with problems arising in the optimal control for fluid-struc- ture interaction systems. Our model consists of a fluid described by the incompressible Navier-Stokes equations interacting with an elastically supported rigid solid. We characterize the structure of the gradient of a cost function to be minimized using a new adjoint problem. The structure of the adjoint system is related to the use of an ALE transverse field introduced in the context of the minimization of non-cylindrical eulerian functionals