This paper discusses modeling of a power-split hybrid electric vehicle and the design of a longitudinal dynamics controller for the University of Waterloo’s self-driving vehicle project. The powertrain of Waterloo’s vehicle platform, a Lincoln MKZ Hybrid, is controlled only by accelerator pedal actuation. The vehicle’s power management strategy cannot be altered, so a novel approach to grey-box modeling of the OEM powertrain control architecture and dynamics was developed. The model uses a time delay neural network (TDNN) to mimic the response of the vehicle’s torque control module and estimate the distribution of torque between the powertrain’s internal combustion engine and electric motors. While related works in the literature have used NNs to design energy management systems for hybrid vehicles, using an NN to emulate an existing vehicle’s torque controller appears to be a unique application. The vehicle’s power-split drivetrain and longitudinal dynamics were modeled using a physics-based analytical approach. All model parameters were identified using Controller Area Network (CAN) data and measurements of wheel torque data that were gathered during vehicle road testing. Using the powertrain model as a framework, a look-ahead linear time-varying (LTV) model predictive controller (MPC) for reference velocity tracking is proposed. Linear MPC for longitudinal vehicle dynamics applications has been explored frequently in the literature; however most work has assumed that torque is applied directly to the wheels without considering powertrain dynamics. The proposed longitudinal controller considers the power-split dynamics by exploiting the structure of the powertrain model. Using some simplifying assumptions about the powertrain dynamics, the system was reformulated as a Hammerstein model. The proposed MPC accounts for the static nonlinear portion of the Hammerstein model by approximating its direct inverse with another NN. Inversion of the nonlinearities allows classical linear MPC algorithms to be applied directly to the linear portion of the system.