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

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.

Reasons for replacing: (i) change of the email of the corresponding author, (ii) added references dor section 2, (iii) minor English corrections, (iv) typos added

References in corpus (1)

• Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems

Cited by in corpus (4)

• Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
• Fractional Order Version of the HJB Equation
• Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
• A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems