A vehicle includes a system and method of modeling and controlling a traction of a wheel of the vehicle. The system includes an observer, a predictive controller and an online solver. The observer receives a dynamic model parameter of the wheel and determines an estimate of a wheel velocity and an uncertainty in the wheel velocity using a non-linear model of the wheel. The predictive controller determines an average gain and differential gain from the estimate of the wheel velocity and the uncertainty in the wheel velocity. The online solver calculates a motor torque and a wheel brake torque for increasing the traction of the wheel with a road based on the average gain and the differential gain. The motor torque and the wheel brake torque are applied at the vehicle.