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arXiv · 1503.07720

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

H. M. Ali·F. Lobo Pereira·S. M. A. Gama
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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.

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H. M. Ali, F. Lobo Pereira, S. M. A. Gama. 2015-04-10. A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems. https://doi.org/10.1002/mma.3811

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