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

• Published in: Mathematical methods in the applied sciences Vol. 39; no. 13; pp. 3640 - 3649
• Main Authors: Ali, Hegagi M., Pereira, Fernando Lobo, Gama, Sílvio M. A.
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 15-09-2016; Wiley Subscription Services, Inc
• Subjects: Caputo fractional derivative; Control problems; Control theory; Differential equations; Fractional differential equations; Fractional optimal control; Functions (mathematics); Mathematical analysis; Maximum principle; Mittag-Leffler function; Nonlinear control; Nonlinearity; Optimal control; Optimization; Performance indices; Production planning
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.3811

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. The approach we use to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems is new in this context. 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. Copyright © 2016 John Wiley & Sons, Ltd.