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Topology-based control design for congested areas in urban networks

By Liudmila Tumash, Carlos Canudas de Wit and Maria Laura Delle Monache

Abstract

International audienceThis 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

Topics: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Publisher: 'Institute of Electrical and Electronics Engineers (IEEE)'
Year: 2020
OAI identifier: oai:HAL:hal-02860455v2
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