Optimal Control Laws for Traffic Control

In this paper we develop optimal control laws for traffic networks. A standard traffic flow model is used to formulate the traffic control in terms of " on-off " strategy for the traffic signals. It is of the form of the optimal bilinear control problem with the binary constraints. We develop a Lyapunov function based feedback law for minimizing traffic congestions and stabilizing the traffic flow. Also, a novel binary optimization method is developed to obtain a real-time optimal control law for the binary constrained optimal control problem. Both methods are tested and compared for a large scale traffic network. Our tests demonstrate that the both method provides very effective but efficient traffic control law.