Pontryagin principle for a Mayer problem governed by a delay functional differential equation

TL;DR

This paper develops Pontryagin's maximum principle for an optimal control problem involving delay differential equations, extending classical methods to systems with delays using resolvent properties.

Contribution

It introduces a Pontryagin principle for Mayer problems governed by delay differential equations, adapting Michel's method and resolvent properties for such systems.

Findings

Established Pontryagin maximum principle for delay systems

Extended Michel's method to functional differential equations

Provided conditions for optimal control with delays

Abstract

We establish Pontryagin principles for a Mayer's optimal control problem governed by a functional differential equation. The control functions are piecewise continuous and the state functions are piecewise continuously differentiable. To do that, we follow the method created by Philippe Michel for systems governed by ordinary differential equations, and we use properties of the resolvent of a linear functional differential equation.