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Boundary and In-Domain 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
Inria Grenoble - Rhône-Alpes, GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : This paper presents a novel approach to design control for traffic on large-scale urban networks by analyzing the structure of one single partial differential equation (PDE). In particular, we elaborate a method that represents a curvilinear coordinate transformation translating a 2D conservation law into a parametrized set of equations each having a structure of inhomogeneous 1D LWR equation. This resulting system can be explicitly analyzed for traffic evolving on urban networks of arbitrary size. As an application example, we demonstrate how the 2D model in curvilinear coordinates can be used to design two different controllers for urban traffic. First, a boundary controller is designed to track any desired space- and timedependent vehicle density profile with the help of HamiltonJacobi formalism. Second, we design an in-domain variable speed limit (VSL) controller that steers traffic flow such that any space-varying equilibrium can be achieved. We validate the control results numerically using the structure of Grenoble downtown.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03167733
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Submitted on : Sunday, October 24, 2021 - 7:13:09 PM
Last modification on : Friday, February 4, 2022 - 3:19:48 AM

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Liudmila Tumash, Carlos Canudas de Wit, Maria Laura Delle Monache. Boundary and In-Domain Control for Large-Scale Urban Traffic Networks. 2021. ⟨hal-03167733v2⟩

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