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Autonomous driving is achieved by controlling the coupled nonlinear longitudinal and lateral vehicle dynamics. Longitudinal control greatly affects lateral dynamics and must preserve lateral stability conditions, while lateral controllers must take into account actuator limits and ride comfort. This work deals with the coordinated longitudinal and lateral control for autonomous driving. An improved particle swarm optimized PID (PSO-PID) is proposed to handle the task of speed tracking based on nonlinear longitudinal dynamics. An enhanced linear parameter varying model predictive controller (LPV-MPC) is also designed to control lateral dynamics, the latter is formulated with an adaptive LPV model in which the tire cornering stiffness coefficients are estimated by a recursive estimator. The proposed LPV-MPC is enhanced with an improved cost function to provide better performance and stability. Matlab/Carsim cosimulations are carried out to validate the proposed controllers.