Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level

This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constrains in the upper level and a finite-dimensional parametric optimization problem in the lower level. After transforming the problem into an equivalent single-level problem we concentrate on the derivation of a necessary optimality condition of Pontryagin-type. We point out some major difficulties arising from the bilevel structure of the original problem and its pure state constraints in the upper level leading to a degenerated maximum principle in the absence of constraint qualifications. Hence, we use a partial penalization approach and a well-known regularity condition for optimal control problems with pure state constraints to ensure the non-degeneracy of the derived maximum principle. Finally, we illustrate the applicability of the derived theory by means of a small example.