Automated vehicles must travel in a given environment detecting, planning, and following a safe path. In order to be safer than humans, they must be able to perform these tasks as well or better than human drivers under different critical conditions. An essential part of the study of automated vehicles is the development of representative models that are accurate and computationally efficient. Thus, to cope with these problems, the present work applies artificial neural networks and system identification methods to perform vehicle modeling and trajectory tracking control. First, neural architectures are used to capture tire characteristics present in the interaction between lateral and longitudinal vehicle dynamics, reducing computational costs for predictive controllers. Secondly, a combination of black-box models is used to improve predictive control. Then, a hybrid approach combines physics-based and data-driven models with black-box modeling of the discrepancies. This approach is chosen to improve the accuracy of vehicle modeling by proposing a discrepancy model to capture mismatches between vehicle models and measured data. Results are shown when the proposed methods are applied to systems with simulated/real data and compared with approaches found in the literature, showing an increase of accuracy (up to 40 percent) in terms of error-based metrics while having lesser computational effort (reduction by up to 88 percent) than conventional predictive controllers.