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

摘要

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