Second-order necessary conditions in optimal control of evolution systems

This paper is devoted to second-order necessary optimality conditions for a class of infinite-dimensional optimal control problems under functional pure state constraints together with end point constraints. Using tools of second-order variational analysis, we derive necessary optimality conditions in the form of a minimum principle and a second-order variational inequality. We further propose sufficient conditions guaranteeing normality of the minimum principle. Finally, applications to optimal control models involving PDEs are provided.