Using Nudging for the Control of a Non-Local PDE Traffic Flow Model

Abstract

The paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with nudging (or “look behind”) terms. The obtained conditions are novel, as they are not covered by existing results in the literature. The paper also provides results which indicate that nudging can increase the flow in a ring-road and, if properly designed, can have a strong stabilizing effect on traffic flow. The efficiency of the use of nudging terms is demonstrated by means of a numerical example.