Topology-based control design for congested areas in urban networks

Liudmila Tumash (1) , Carlos Canudas de Wit (1) , Maria Laura Delle Monache (1)

1 NECS - Networked Controlled Systems

This paper addresses the problem of a boundary control design for traffic evolving in a large urban network. The traffic state is described on a macroscopic scale and corresponds to the vehicle density, whose dynamics are governed by a two dimensional conservation law. We aim at designing a boundary control law such that the throughput of vehicles in a congested area is maximized. Thereby, the only knowledge we use is the network's topology, capacities of its roads and speed limits. In order to achieve this goal, we treat a 2D equation as a set of 1D equations by introducing curvilinear coordinates satisfying special properties. The theoretical results are verified on a numerical example, where an initially fully congested area is driven to a state with maximum possible throughput.

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]

Liudmila Tumash, Carlos Canudas de Wit, Maria Laura Delle Monache. Topology-based control design for congested areas in urban networks. The 23rd IEEE International Conference on Intelligent Transportation Systems, Sep 2020, Rhodos, Greece. ⟨hal-02860455v1⟩