Tracking Perimeter Control for Two-Region Macroscopic Traffic Dynamics: An Adaptive Dynamic Programming Approach

Leveraging the concept of the macroscopic fundamental diagram (MFD) concept, perimeter control can be implemented in some identified critical intersections to alleviate network-level congestion effectively. Considering the time-varying nature of the travel demand pattern and the equilibrium of the accumulation state, we reformulate the conventional set-point perimeter control (SPC) problem for the two-region MFD system into an optimal tracking perimeter control problem (OTPCP). Unlike the SPC schemes that stabilize the traffic dynamics to the desired equilibrium point, the proposed tracking perimeter control (TPC) scheme will regulate the traffic dynamics to a desired trajectory in a differential framework. Due to the inherent network uncertainties, such as uncertain dynamics of heterogeneity and demand disturbance, the system dynamics could be uncertain or even unknown. To address these issues, we propose an adaptive dynamic programming (ADP) approach to solving the OTPCP without utilizing knowledge of the system dynamics. Finally, numerical experiments demonstrate the effectiveness of the proposed ADP-based TPC. Compared with the SPC scheme, the proposed TPC scheme achieves a 20.01% reduction in total travel time and a 3.15% improvement in cumulative trip completion in our case study.