Boundary Controllability and Asymptotic Stabilization of a Nonlocal Traffic Flow Model

Bayen A, Coron JM, De Nitti N, Keimer A, Pflug L (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Abstract

We study the exact boundary controllability of a class of nonlocal conservation laws modeling traffic flow. The velocity of the macroscopic dynamics depends on a weighted average of the traffic density ahead and the averaging kernel is of exponential type. Under specific assumptions, we show that the boundary controls can be used to steer the system towards a target final state or out-flux. The regularizing effect of the nonlocal term, which leads to the uniqueness of weak solutions, enables us to prove that the exact controllability is equivalent to the existence of weak solutions to the backwards-in-time problem. We also study steady states and the long-time behavior of the solution under specific boundary conditions.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Lukas Pflug FAU Competence Center Scientific Computing (FAU CSC)

Involved external institutions

University of California, Berkeley

United States (USA) (US) University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne

France (FR)

How to cite

APA:

Bayen, A., Coron, J.-M., De Nitti, N., Keimer, A., & Pflug, L. (2021). Boundary Controllability and Asymptotic Stabilization of a Nonlocal Traffic Flow Model. Vietnam Journal of Mathematics. https://doi.org/10.1007/s10013-021-00506-7

MLA:

Bayen, Alexandre, et al. "Boundary Controllability and Asymptotic Stabilization of a Nonlocal Traffic Flow Model." Vietnam Journal of Mathematics (2021).

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