# PDE-Based Feedback Control of Freeway Traffic Flow via Time-Gap Manipulation of ACC-Equipped Vehicles

## TL;DR

This paper presents a PDE-based feedback control method for stabilizing congested freeway traffic flow by manipulating the time-gap of ACC vehicles, improving efficiency and comfort.

## Contribution

It introduces a novel control design for a PDE traffic model that stabilizes congested flow using in-domain actuation via ACC vehicle time-gap adjustments.

## Key findings

- Stability of the traffic flow is achieved through a Lyapunov-based feedback law.
- Convective stability is demonstrated using an input-output approach.
- Simulation results show improved fuel efficiency, travel time, and comfort.

## Abstract

We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise Control-equipped) and manual vehicles. The control input is the value of the time-gap setting of ACC-equipped and connected vehicles, which gives rise to a problem of control of a 2x2 nonlinear system of first-order hyperbolic PDEs with in-domain actuation. The feedback law is designed in order to stabilize the linearized system, around a uniform, congested equilibrium profile. Stability of the closed-loop system under the developed control law is shown constructing a Lyapunov functional. Convective stability is also proved adopting an input-output approach. The performance improvement of the closed-loop system under the proposed strategy is illustrated in simulation, also employing four different metrics, which quantify the performance in terms of fuel consumption, total travel time, and comfort.