Optimal Feedback Control for Leray and Navier–Stokes Alpha Models

Abstract

The existence of an optimal feedback control for the Leray alpha model and the Navier–Stokes alpha model is proved. The control of external forces that depend on the fluid velocity is considered. As a result, the control function can be chosen more accurately, since, in this case, it is chosen not from a finite set of available controls, but belongs to the image of a multivalued mapping. The existence of an optimal solution minimizing a specified bounded lower semicontinuous quality functional is proved by applying the topological approximation method for studying hydrodynamic problems.