A Note on Optimality Conditions for Control Problems with Parameters

In this paper we study optimal control problems characterized by two different kinds of decision instruments: control functions and pa- rameters. The former are piecewise continuous functions, the latter are constants in the whole programming interval. We suggest that, even if the theory for these problems has been developed a few decades ago, the standard sufficient conditions are not completely satisfactory. The critical issue is strictly connected with the approach used to prove the necessary conditions. A historical review of these conditions contextu- alizes our discussion. We believe that the sufficiency issue for this class of problems is still open to developments.