Coupled Points for Infinite-Dimensional Control Systems

In this paper we introduce the definition of coupled points for a linear problem with quadratic cost in optimal control in reflexive Banach spaces, where both endpoints are allowed to vary in subspaces. Furthermore we introduce the concepts of normality and strong normality to obtain a new necessary condition in terms of coupled points. Using these results we get a new second order necessary condition for a general optimal control problem in reflexive Banach spaces.