Analysis and control of a non-local PDE traffic flow model

Abstract

This paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring road with possible nudging (or ‘look behind’) terms. The obtained conditions are novel, as they are not covered by existing results in the literature. This paper also provides results which indicate that nudging can increase the flow in a ring road and, if properly designed, can have a strong stabilising effect on traffic flow. More specifically, this paper gives results that guarantee local exponential stability of the uniform equilibrium profile in the state norm even for cases where the uniform equilibrium profile in a ring road without nudging is not asymptotically stable and the model admits density waves. The efficiency of the use of nudging terms is demonstrated by means of a numerical example.