Value function and necessary conditions in optimal control problems for differential-difference inclusions Original Research Article

This paper deals with the optimal control problems for differential-difference inclusions subject to endpoint constraints. We follow a twofold goal. First, we develop a method for estimating the generalized gradients of value function in the problems above. Second, we use these estimates for obtaining necessary optimality conditions. The results obtained are expressed in terms of Clarke constructions for nonsmooth mappings and sets.