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

TL;DR

This paper introduces a Hamiltonian framework for sufficient conditions in optimal control, extending existing theories to minimal regularity settings and incorporating super Hamiltonians for broader applicability.

Contribution

It develops a Hamiltonian approach under minimal regularity assumptions and introduces the concept of super Hamiltonians, expanding the theoretical foundation of optimal control.

Findings

Encompasses many known results in optimal control

Provides a framework for problems with minimal regularity

Introduces super Hamiltonian concept for broader analysis

Abstract

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.