  Many application models in quantum physics and chemistry require to control
multi-electron systems to achieve a desired target configuration. This
challenging task appears possible in the framework of time-dependent density
functional theory (TDDFT) that allows to describe these systems while avoiding
the high dimensionality resulting from the multi-particle Schr\"{o}dinger
equation. For this purpose, the theory and numerical solution of optimal
control problems governed by a Kohn-Sham TDDFT model are investigated,
considering different objectives and a bilinear control mechanism. Existence of
optimal control solutions and their characterization as solutions to Kohn-Sham
TDDFT optimality systems are discussed. To validate this control framework, a
time-splitting discretization of the optimality systems and a nonlinear
conjugate gradient scheme are implemented. Results of numerical experiments
demonstrate the computational capability of the proposed control approach.
