Aerial refueling has demonstrated significant benefits to aviation by extending the range and endurance of aircraft [1]. The development of autonomous aerial refueling (AAR) techniques for unmanned aerial vehicles (UAVs) makes new missions and capabilities possible [2], like the ability for long range or long time flight. As the most widely used aerial refueling method, the probedrogue refueling (PDR) system is considered to be more flexible and compact than other refueling systems. However, a drawback of PDR is that the drogue is passive and susceptible to aerodynamic disturbances [3]. Therefore, it is difficult to design an AAR system to control the probe on the receiver to capture the moving drogue within centimeter level in the docking stage.It used to be thought that the aerodynamic disturbances in the aerial refueling mainly include the tanker vortex, wind gust, and atmospheric turbulence. According to NASA Autonomous Aerial Refueling Demonstration (AARD) project [2], the forebody flow field of the receiver may also significantly affect the docking control of AAR, which is called "the bow wave effect" [4]. As a result, the modeling and simulation methods for the bow wave effect were studied in our previous works [5,6].Since the obtained mathematical models are somewhat complex and there may be some uncertain factors in practice, this paper aims to use a model-free method to compensate for the docking error caused by aerodynamic disturbances including the bow wave effect.Most of the existing studies on AAR docking control do not consider the bow wave effect. In [7][8][9], the drogue is assumed to be relatively static (or oscillates around the equilibrium) and not affected by the flow field of the receiver forebody. However, in practice, the receiver aircraft is affected by aerodynamic disturbances, and the drogue is affected by both the wind disturbances and the receiver forebody bow wave. As a major difficulty in the control of AAR, the aerodynamic disturbances, especially the bow wave effect, attract increasing attention in these years. In [10,11], the wind effects from the tanker vortex, the wind gust, and the atmospheric turbulence are analyzed, and in [5,6,12], the modeling and simulation methods for the receiver forebody bow wave effect are studied, but no control methods are proposed. In [4], simulations show that the bow wave effect can be compensated by adding an offset value to the reference trajectory, but the method for obtaining the offset value is not given.