Pontryagin optimality conditions for generalized bilevel optimal control problems with pure state inequality constraints

In this paper, we study a generalized bilevel optimal control problem that has a variational inequality parametrized by the final state on the follower and pure state constraints on the leader.After reducing the problem with a gap function to an analogous single-level optimal control problem, we focus on the development of a necessary optimality condition of the Pontryagin type.We highlight some significant issues originating from the generalized bilevel structure and its pure state constraints on the leader, which give rise to a degenerated maximum principle in the absence of constraint qualifications.To ensure the nondegeneracy of the derived maximum principle, we employ a partial penalization strategy and a well-known regularity criterion for optimal control problems with pure state constraints.