Developing methods for autonomous landing of an unmanned aerial vehicle (UAV) on a mobile platform has been an active area of research over the past decade, as it offers an attractive solution for cases where rapid deployment and recovery of a fleet of UAVs, continuous flight tasks, extended operational ranges, and mobile recharging stations are desired. In this work, we present a new autonomous landing method that can be implemented on micro UAVs that require high-bandwidth feedback control loops for safe landing under various uncertainties and wind disturbances. We present our system architecture, including dynamic modeling of the UAV with a gimbaled camera, implementation of a Kalman filter for optimal localization of the mobile platform, and development of model predictive control (MPC), for guidance of UAVs. We demonstrate autonomous landing with an error of less than 37 cm from the center of a mobile platform traveling at a speed of up to 12 m/s under the condition of noisy measurements and wind disturbances.