Autonomous Vehicles Driving Traffic: The Cauchy Problem

TL;DR

This paper studies a mathematical model combining traffic flow equations with autonomous vehicle dynamics, proving that solutions exist globally over time under certain conditions.

Contribution

It introduces a coupled PDE-ODE model for autonomous vehicle traffic control and establishes a global existence theorem for its solutions.

Findings

Proves global in time existence of solutions.

Models autonomous vehicle influence on traffic flow.

Provides a rigorous mathematical framework for AV traffic control.

Abstract

This paper deals with the Cauchy Problem for a PDE-ODE model, where a system of two conservation laws, namely the Two-Phase macroscopic model, is coupled with an ordinary differential equation describing the trajectory of an autonomous vehicle (AV), which aims to control the traffic flow. Under suitable assumptions, we prove a global in time existence result.