A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems

TL;DR

This paper introduces a novel formulation and necessary optimality conditions for fractional nonlinear control problems, employing a generalized Mittag-Leffler function for solutions, demonstrated through a simple example.

Contribution

It presents a new approach to derive Pontryagin maximum principle conditions for fractional control problems with Caputo derivatives and introduces a generalized Mittag-Leffler function method for solving them.

Findings

Established necessary optimality conditions for fractional control problems.

Developed a new solution method using generalized Mittag-Leffler functions.

Validated the approach with a simple illustrative example.

Abstract

In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. We use a new approach to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems. Moreover, a new method based on a generalization of the Mittag-Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result.