Model Predictive Control for Urban Traffic Signals with Stability Guarantees

Traditional traffic signal control focuses more on the optimization aspects whereas the stability and robustness of the closed-loop system are less studied. This paper aims to establish the stability properties of traffic signal control systems through the analysis of a practical model predictive control (MPC) scheme, which models the traffic network with the conservation of vehicles based on a store-and forward model and attempts to balance the traffic densities. More precisely, this scheme guarantees the exponential stability of the closed-loop system under state and input constraints when the inflow is feasible and traffic demand can be fully accessed. Practical exponential stability is achieved in case of small uncertain traffic demand by a modification of the previous scheme. Simulation results of a small-scale traffic network validate the theoretical analysis.