Lyapunov stabilization of a nonlocal LWR traffic flow model

TL;DR

This paper develops a Lyapunov-based control method for a nonlocal LWR traffic flow model, enabling stabilization of traffic velocity towards equilibrium with explicit convergence rates, demonstrated through numerical examples.

Contribution

It introduces a Lyapunov function for controlling nonlocal traffic flow models and derives explicit convergence rates towards equilibrium velocities.

Findings

Explicit Lyapunov function for nonlocal traffic flow stabilization

Derived convergence rate towards equilibrium velocity

Numerical validation of theoretical results

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.