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

arXiv: https://arxiv.org/abs/1812.08154 · HTML: https://mlsanity.com/paper/1812.08154/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2018.

## Built on by (most cited first, 2 of 2)

- [Proximal Policy Optimization Learning based Control of Congested Freeway Traffic](https://mlsanity.com/paper/2204.05627/) (2022)
- [Reinforcement Learning for Freeway Lane-Change Regulation via Connected Vehicles](https://mlsanity.com/paper/2412.04341/) (2024)

## Abstract (arXiv)

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.