Biblio

We consider global stability of a flow network model for vehicular traffic. Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions. In this paper, we show that the network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity allows us to prove global asymptotic stability by embedding the system in a larger system that is monotone.

We study the control of monotone systems when the objective is to maintain trajectories in a directed set (that is, either upper or lower set) within a signal space. We define the notion of a directed alternating simulation relation and show how it can be used to tackle common bottlenecks in abstraction-based controller synthesis. First, we develop sparse abstractions to speed up the controller synthesis procedure by reducing the number of transitions. Next, we enable a compositional synthesis approach by employing directed assume-guarantee contracts between systems. In a vehicle traffic network example, we synthesize an intersection signal controller while dramatically reducing runtime and memory requirements compared to previous approaches.