A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I

In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super Hamiltonian (i.e. a Hamiltonian which is greater then or equal to the maximised one) on the other we develop the theory under some minimal regularity assumptions. The results we present enclose many known results and they can be used to tackle new problems.