Coordinated Model Predictive Controllers With Stabilizing Reference for Traffic Signals in Urban Road Network

A model based distributed control for traffic signals in a road network is considered from the views of optimality and stability. The nonlinear cell transmission model is used for predicting the traffic dynamics along each link carrying the traffic from one intersection to another. In the proposed control approach, each local controller solves a local optimization problem selecting the switching times of the traffic light at the controlled intersection over a finite prediction horizon using estimates of the local traffic state and information received from neighbouring intersections. A stabilizing rule inspired by the stability proof of max-pressure control is proposed for the congested traffic conditions. This stabilizing rule is then treated as a reference for the proposed coordinated model predictive controller. A constraint related to the value of the Lyapunov function under this stabilizing reference is then introduced to each local optimization whenever the local Lyapunov function at the controlled intersection or its neighbour exceeds the threshold. This constrained local optimization problem is shown to be feasible all the time due to the existence of the proposed stabilizing rule and is effective to decrease the global Lyapunov function. The proposed coordinated model predictive control with stabilizing reference is completely independent of a prior knowledge on the traffic demand. This paper shows by simulations that combining a stabilizing max-pressure based reference with coordinated model predictive control (CMPC) helps in avoiding the instability problem observed for pure CMPC when the traffic load becomes very high (but does not exceed the stability bounds which guarantee good performance of max-pressure based controls).