In recent years, connected vehicles (CVs) and automated vehicles (AVs) have emerged as a realistic and viable transportation option. Research centers and companies have dedicated substantial efforts to the technology, motivated largely by the potential safety benefits that can be realized through the elimination of human error, the enhancement of mobility via reduction of congestion and optimization of trips, and the associated positive environmental impacts. Both sensors and control mechanisms are needed for this technology to succeed. The goal of this study is to make use of vehicle connectivity via vehicle-to-vehicle (V2V) (i.e., exchanging information between vehicles) and vehicle-to-infrastructure (V2I) (i.e., exchanging information with the infrastructure, including intersection controllers) features, leveraging both connected and automated capabilities, to develop control algorithms/systems that deliver solutions/recommendations for connected automated vehicles (CAVs) [1] as they proceed through intersections. The algorithms developed in this report deliver optimal and/or near-optimal solutions, which required extensive simulations and field experiments for validation. In the work described in this report, the research group combined mathematical modeling, optimal control theory, and optimization into a simulation framework that allows vehicles to cross an intersection safely, while incurring the least amount of delay. These models feature kinematic, dynamic and static constraints. Different versions of the model were developed, ranging from exact solutions that cannot be implemented in real-time to heuristic solutions that are computationally efficient. The results of the final proposed model were compared to other control techniques already implemented in the field, and demonstrated that a reduction of at least 50% in delay was achievable. An interesting byproduct of this model was the reduction in fuel consumption, and thus emissions, by more than 10%.