Necessary optimality conditions for bilevel dynamic problems

We study the bilevel dynamic problem, which is a hierarchy of two dynamic optimization problems where the constraint region of the upper level problem is determined implicitly by the solutions to the lower level optimal control problem. Sensitivity analysis of the lower level problem with respect to the L¹ perturbation in the upper level decision variable is given and first order necessary optimality conditions are derived by formulating the bilevel dynamic problem as a single level optimal control problem that involves the value function of the lower level problem. A constraint qualification of calmness type and a sufficient condition for the calmness are also given