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Fixed-wind unmanned aerial vehicles (UAVs) are essential for low cost aerial surveillance and mapping applications in remote regions. One of the main limitations of UAVs is limited fuel capacity and hence requires periodic refueling to accomplish a mission. The usual mechanism of commanding the UAV to return to a stationary base station for refueling can result in fuel wastage and inefficient mission operation time. Alternatively, unmanned gound vehicle (UGV) can be used as a mobile refueling unit where the UAV will rendezvous with the UGV for refueling. In order to accurately perform this task in the presence of wind disturbances, we need to determine an optimal trajectory in 3D taking UAV and UGV dynamics and kinematics into account. In this paper, we propose an optimal control formulation to generate a tunable UAV trajectory for rendezvous on a moving UGV taking wind disturbances into account. By a suitable choice of the value of an aggressiveness index in our problem setting, we are able to control the UAV rendezvous behavior. Several numerical results are presented to show the reliability and effectiveness of our approach. I. INTRODUCTIONFixed-wing unmanned aerial vehicles (UAVs) are essential components of remote monitoring applications like surveillance, mapping, aerial photography, etc., where the UAVs need to cover large regions. Typical UAVs used for these applications are of low cost with limited fuel capacity and hence require periodic refueling to accomplish the mission. For the case of using low cost

Communicated by M. A. LachowiczIn 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.