TITLE: Renormalized Solutions for Optimal Control of the Drift in Fokker-Planck Equations
 

ABSTRACT: We consider a bilinear optimal control problem subject to a Fokker-Planck equation, where the control acts as the temporal amplitude of a given spatial vector field in the first-order drift term. The problem setup regarding the spatial vector field is going to be very restrictive, so we cannot rely on the usual energy methods; this is motivated by applications. We thus propose to work with a renormalized concept of solutions here, which is however inherently nonlinear and thus in principle not compatible with established optimal control theory. It will be shown how to overcome these issues and how to establish optimality conditions for the optimal control problem.