Boundary and VSL Control for Large-Scale Urban Traffic Networks

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

1 DANCE - Dynamics and Control of Networks

This paper presents a unique method that considerably simplifies control design for traffic systems evolving in large-scale networks. In particular, we present a coordinate transformation that translates a 2D continuous traffic model based on a conservation law into a continuous set of equations with a structure similar to the classical LWR equation. Then for this system we explicitly design a boundary controller that drives the state to any space-and time-dependent desired trajectory. The desired state admits traffic regimes switching, i.e., it can be partially in free-flow and partially congested. Then we pose a different control task of stabilizing a system to quite any space-varying equilibrium. For that we design a variable speed limit (VSL) controller elaborating intrinsic properties of the model. The main peculiarity of both controls is that they require only the knowledge about the network geometry and the fundamental diagram. We validate the results numerically using the network of Grenoble.

Mots clés: Boundary control; Hamilton-Jacobi; partial differential equations; urban traffic control; variable speed limit

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Liudmila Tumash, Carlos Canudas de Wit, Maria Laura Delle Monache. Boundary and VSL Control for Large-Scale Urban Traffic Networks. 2021. ⟨hal-03167733v1⟩