The development of autonomous and intelligent vehicles is increasing continuously in the aim to reach a reliable and secured transportation system. Indeed, autonomous navigation include three main steps: perception and localization, planning and control. This thesis covers essentially the study of the vehicle modeling and the vehicle control, focused on the coupled lateral and longitudinal control of the autonomous racing vehicle. Three different control strategies are considered: First one based on coupled control while the second one is decoupled control. In coupled controller, adaptive model predictive control (MPC) is used which handles both lateral and longitudinal control. In the decoupled control strategy, longitudinal dynamics is controlled with the help of a PID and Lateral dynamics is controlled first with MPC and second with Lateral controller.