A sufficient optimality condition for non-linear delayed optimal control problems

TL;DR

This paper establishes a sufficient optimality condition for non-linear delayed optimal control problems by transforming them into equivalent non-delayed problems and verifying a Hamilton-Jacobi PDE.

Contribution

It introduces a novel transformation technique that converts delayed control problems into non-delayed ones, enabling the application of Hamilton-Jacobi theory for optimality conditions.

Findings

Provides a new method to handle delays in control problems

Derives a Hamilton-Jacobi PDE for delayed systems

Enables verification of optimality via PDE solutions

Abstract

We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained through a transformation that allow us to rewrite a delayed optimal control problem as an equivalent non-delayed one.