First and second order optimality conditions for optimal control problems of state constrained integral equations

TL;DR

This paper establishes first and second-order necessary and sufficient optimality conditions for control problems involving integral equations with high-order state constraints, advancing the theoretical framework for such constrained control systems.

Contribution

It introduces a novel approach to define and analyze high-order state constraints in integral dynamics, deriving comprehensive optimality conditions.

Findings

Derived first-order necessary conditions for high-order state constraints.

Established second-order necessary and sufficient optimality conditions.

Extended the theoretical understanding of control problems with integral equations.

Abstract

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions.