Lyapunov stabilization of a nonlocal LWR traffic flow model

Jan Friedrich

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arXiv · 2210.02309

Lyapunov stabilization of a nonlocal LWR traffic flow model

Jan Friedrich

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Abstract

Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the nonlocal velocity towards a given equilibrium velocity. Therefore, we present a Lyapunov function measuring the $L^2$ distance between these velocities. We compute the explicit rate at which the system tends towards the stationary speed. The traffic is controlled by a leading vehicle. Numerical examples demonstrate the theoretical results and possible extensions of them.

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Jan Friedrich. 2022-10-05. Lyapunov stabilization of a nonlocal LWR traffic flow model. https://arxiv.org/abs/2210.02309

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