Lyapunov stabilization of a nonlocal LWR traffic flow model

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.