This study deals with the optimal control of hybrid energy storage systems for electric vehicle applications. These storage systems can capitalize on the high specific energy of Lithium-Ion batteries and the high specific power of modern ultracapacitors. The new predictive algorithm uses a state-based approach inspired by power systems optimization, organized as a probability-weighted Markov process to predict future load demands. Decisions on power sharing are made in real time, based on the predictions and probabilities of state trajectories along with associated system losses. Detailed simulations comparing various power sharing algorithms are presented, along with converter-level simulations presenting the response characteristics of power sharing scenarios. The full hybrid storage system along with the mechanical drivetrain is implemented and validated experimentally on a 500 W, 50 V system with a programmable drive cycle having a strong regenerative component. It is experimentally shown that the hybrid energy storage system runs more efficiently and captures the excess regenerative energy that is otherwise dissipated in the mechanical brakes due to the battery's limited charge current capability.