# Feedback Control of Scalar Conservation Laws with Application to Density Control in Freeways by Means of Variable Speed Limits

arXiv: https://arxiv.org/abs/1802.08583 · HTML: https://mlsanity.com/paper/1802.08583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2018.

## Built on by (most cited first, 1 of 1)

- [DVS-RG: Differential Variable Speed Limits Control using Deep Reinforcement Learning with Graph State Representation](https://mlsanity.com/paper/2405.09163/) (2024)

## Abstract (arXiv)

The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are studied: the problem with free speed limits at the inlet and the problem with no speed limits at the inlet. Explicit formulas are provided for respective feedback laws that guarantee stabilization of the desired equilibrium profile. For the first problem, global asymptotic stabilization is achieved; while for the second problem, regional exponential stabilization is achieved. Moreover, the solutions for the corresponding closed-loop systems are guaranteed to be classical solutions, i.e., there are no shocks. The obtained results are illustrated by means of a numerical example.