Min-max and min-min stackelberg strategies with closed-loop information structure
Journal of Dynamical and Control Systems
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In this paper 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. To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that involves the value function of the lower-level problem. Sensitivity analysis of the lower-level problem with respect to the perturbation in the upper-level decision variable is given and first-order necessary optimality conditions are derived by using nonsmooth analysis. A constraint qualification of calmness type and a sufficient condition for the calmness are also given.