Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem

TL;DR

This paper extends fractional optimal control theory with Caputo derivatives by deriving a Noether-like theorem, linking symmetries to conservation laws in fractional variational problems.

Contribution

It introduces a novel Noether-like theorem for fractional optimal control problems using Caputo derivatives, building on Agrawal's Euler-Lagrange conditions.

Findings

Establishes a fractional Noether theorem for Caputo derivatives.

Connects symmetries to conservation laws in fractional control.

Provides a theoretical framework for fractional variational problems.

Abstract

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal's necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal's Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for fractional optimal control problems in the sense of Caputo.