The paper presents a new big data based control design for autonomous vehicles. The main contribution of this work is the longitudinal velocity optimization process, which is based on the approximation of the reachability sets of a passenger vehicle by using a machine-learning approach. The data, which is used for the approximation, is provided by the high-fidelity car simulation software, CarSim. The approximation is performed by applying a well-known decision tree algorithm, C4.5. The reachability sets are computed for different longitudinal velocities. Moreover, a LPV technique based lateral control design is proposed, which is used to guarantee the trajectory tracking of the vehicle. To enhance the capability of the LPV controller, the control scheme is extended with the longitudinal velocity optimization process. Thus, the stable and safe motion of the vehicle is guaranteed.