Strong local optimality conditions for control problems with mixed state-control constraints

In this paper first- and second-order optimality conditions for strong local minimum are presented for optimal control problems with mixed state and control inclusion and equality constraints. The first-order condition is of Pontryagin type, while the second-order condition is of the form of an accessory problem associated with the strong local minimality. This latter condition contains an extra term reflecting the presence of the mixed state-control constraints.