  The mathematical modeling of numerous real-world applications results in
hierarchical optimization problems with two decision makers where at least one
of them has to solve an optimal control problem of ordinary or partial
differential equations. Such models are referred to as bilevel optimal control
problems. Here, we first review some different features of bilevel optimal
control including important applications, existence results, solution
approaches, and optimality conditions. Afterwards, we focus on a specific
problem class where parameters appearing in the objective functional of an
optimal control problem of partial differential equations have to be
reconstructed. After verifying the existence of solutions, necessary optimality
conditions are derived by exploiting the optimal value function of the
underlying parametric optimal control problem in the context of a relaxation
approach.
