System and methods for controlling the oscillation of floating ground stations in aerial wind turbine systems are disclosed. Thrusters on the ground station or on one or more aerial vehicles associated with the ground station apply a compensatory force to the oscillating ground station to reduce and/or substantially eliminate wave-induced oscillations. Submerged thrusters may also rotate the ground station to a preferred alignment direction with the waves. Additionally, control systems use environmental and/or positional sensor data to develop a predictive force profile that maps desired compensatory force magnitude versus time. The control systems use that predictive force profile to direct the thrusters to apply a varying compensatory force over time.