Optimal coupled and decoupled perimeter control in one-region cities

Perimeter controllers, located at a regional border, can manipulate the transfer flows across the border to optimize the regional operational performance. The macroscopic fundamental diagram (MFD), that relates average flow with accumulation, is used to model the traffic flow dynamics. In this paper, two cases of perimeter control inputs are considered: coupled and decoupled control. For both cases, the explicit formulations of the optimal feedback control policies and proofs of optimality are provided for three criteria. The proofs are based on the modified Krotov-Bellman sufficient conditions of optimality, where the upper and lower bounds of state variables are calculated.