Necessary optimality conditions in a non-smooth control problem for Volterra type discrete systems

The optimal control problem described by the difference analog of the Volterra type integro-differential equation with a non-differentiable quality criterion is considered. It is assumed that the right-hand side of the original equation and the quality functional with respect to the state vector have derivatives in any direction. First, using the increment method and taking into account some concepts of non-smooth analysis, the necessary optimality conditions are established in terms of derivatives in directions of a general nature. Then, based on them, the necessary optimality conditions directly expressed through the parameters of the non-smooth problem under consideration are established.