Necessary conditions for functional differential inclusions

We consider an optimal control problem in which the dynamic equation and cost function depend on the recent past of the trajectory. The regularity assumed in the basic data is Lipschitz continuity with respect to the sup norm. It is shown that, for a given optimal solution, an adjoint arc of bounded variation exists that satisfies an associated Hamiltonian inclusion. From this result, known smooth versions of the Pontryagin maximum principle for hereditary problems can be easily derived. Problems with Euclidean endpoint constraints are also considered.