Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level
研究了上层含纯状态约束、下层为有限维参数优化问题的双层最优控制问题，推导了非退化的庞特里亚金型最优性条件，并用小例子验证了理论。
This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constraints 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 nondegeneracy of the derived maximum principle. Finally, we illustrate the applicability of the derived theory by means of a small example.