A system control a vehicle using a friction function describing a friction between a type of surface of the road and a tire of the vehicle as a function of a slip of a wheel of the vehicle. The parameters of each friction function include an initial slope of the friction function defining a stiffness of the tire and one or combination of a peak friction, a shape factor and a curvature factor of the friction function. Upon estimating a slip and a stiffness of the tire, the system selects from the memory parameters of the friction function corresponding to the current stiffness of the tire, determines a control command using a value of the friction corresponding to the slip of the tire according to the friction function defined by the selected parameters, and submits the control command to an actuator of the vehicle.