An important part of building an autonomous mobile control system is creating a model that accurately reflects the system's behavior in order to predict and plan the future state of the system. Several approaches to building a model of an autonomous vehicle have been implemented and studied. However, the trade-off between the accuracy and computation time of a model makes it difficult for an autonomous system to use accurate models in real-time to plan its trajectory. In the research presented in this paper, we use system identification to develop a model that accurately predicts the trajectory of the vehicle while reducing the computation time of the model. This model is built from experimental data collected from the CAT Vehicle at the University of Arizona. Our model is implemented on a hybrid predictive controller and tested in simulations and real-world applications. The controller uses the model to follow a planned trajectory and avoid obstacles in the state space with reasonable computation time. While the proposed model is specific to a particular autonomous vehicle, our methods and models could be applied to other autonomous systems.