Semivectorial bilevel optimal control problems: existence results

We consider a bilevel optimal control problem where the upper level, to be solved by a leader, is a scalar optimal control problem and the lower level, to be solved by several followers, is a multiobjective convex optimal control problem. We deal with the so-called optimistic case, when the followers are assumed to choose a best choice for the leader among their best responses, as well with the so-called pessimistic case, when the best response chosen by the followers can be the worst choice for the leader. We present sucient conditions on the data for existence of solutions to both the optimistic and pessimistic optimal control problems, with particular attention to the linear-quadratic case.