Second-Order Necessary/Sufficient Conditions for Optimal Control Problems in the Absence of Linear Structure

TL;DR

This paper explores second-order optimality conditions in control problems without relying on linear structures, providing both necessary and sufficient conditions for local optimality.

Contribution

It introduces second-order conditions for optimal control problems that do not depend on linearity, extending the theoretical framework of optimality criteria.

Findings

Derived second-order necessary conditions for control problems.

Established a sufficient condition for local minimizers.

Extended the theory beyond linear-structure assumptions.

Abstract

Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient condition for a local minimizer is also given.