OPTIMAL BILINEAR CONTROL FOR THE X-RAY FREE ELECTRON LASER SCHRODINGER EQUATION

摘要

In this paper, we consider an optimal bilinear control problem for the nonlinear Schrodinger equation with a time-dependent electromagnetic field and a Coulomb potential, which arises as an effective single particle model in X-ray free electron lasers (XFELs). We show the well-posedness of the problem and the existence of an optimal control. We prove the Frechet-differentiability of the objective functional and give a precise characterization for the optimal control by the first order optimality system.