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

作者：Ali Hegagi M^*; Pereira Fernando Lobo; Gama Silvio M A

来源：Mathematical Methods in the Applied Sciences, 2016, 39(13): 3640-3649.

DOI：10.1002/mma.3811

• Fractional differential equations
• Control problems
• Caputo fractional derivative
• Fractional optimal control
• Mittag-Leffler function

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.

• 出版日期2016-9-15