Alberto Castro, in Handbook of Materials Modeling : Methods: Theory and Modeling (Wanda Andreoni and Sidney Yip, eds.), 1-21 (Springer, Cham, 2018)

Optimal control theory (OCT) is a branch of mathematics that deals with the problem of finding optimal trajectories for dynamical systems. It can be used in combination with time dependent quantum mechanical methods that describe the evolution of the electronic and/or nuclear wave functions of atoms, molecules, or materials in the presence of external perturbations, such as electromagnetic fields. OCT may then find the optimal shape of those external perturbations: the optimal character is defined in terms of a functional of the behavior of the system. This chapter provides a brief description of the basic elements of the theory and an overview of its applications to quantum dynamics and electronic structure.