Studies on transportation management systems have undergone several waves of advancement in both theory and practice. One challenge inhibiting the development of the next-generation intelligent transportation system is the disparity in two relevant academic fields: control system engineering and transportation science. My research bridged this gap by applying advanced Partial Differential Equation control, optimization, and reinforcement learning techniques to various traffic problems that are modeled by the macroscopic traffic flow model. My research focused on studying the intelligent traffic flow system with connected and automated vehicles and developing control algorithms for traffic management infrastructures. In this talk, I will start with control problem of stop-and-go traffic, a common phenomenon that has drawn a lot of research interests over the years since it leads to acceleration-deceleration activities of drivers, increased fuel consumption, and greater risk. I will show a methodological PDE model-based control framework for boundary actuation and estimation of such a problem. To optimize the traffic performance that cannot be described with models, I will apply Extremum Seeking design which is a real-time, model-free, adaptive optimization approach. Reinforcement Learning (RL) approach will also be introduced to enable model-free control of traffic flow system through a complete data-driven process and will then be compared with the model-based control approaches with rigorous theoretical guarantees.