Formal Synthesis of Distributed Optimal Traffic Control Policies

We propose a formal methods approach to control traffic signals optimally from specifications described by metric temporal logic (MTL). Since real-time optimization is computationally infeasible beyond small-scale networks, we use a divide and conquer approach. We decompose the network into smaller subnetworks and synthesize assume-guarantee contracts for their interconnections. We show how to exploit mathematical properties of traffic dynamics to find time varying contracts by solving a constraint satisfaction problem. A model predictive control (MPC) approach is used to find local controls for each subnetwork to minimize induced delays, while assume-guarantee contracts and appropriately designed terminal constraints ensure the satisfaction of the specification all over the network. We present a case study on an urban traffic network.