# Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles

arXiv: https://arxiv.org/abs/1807.11476 · HTML: https://mlsanity.com/paper/1807.11476/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2018.

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

- [On kernel-based statistical learning in the mean field limit](https://mlsanity.com/paper/2310.18074/) (2023)
- [Data/moment-driven approaches for fast predictive control of collective dynamics](https://mlsanity.com/paper/2402.15611/) (2024)

## Abstract (arXiv)

We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of vehicle-to-vehicle interactions and then upscaled to the global flow via a kinetic approach based on a Boltzmann-type equation. Then first and second order hydrodynamic traffic models, which naturally embed the microscopic control strategies, are consistently derived from the kinetic-controlled framework via suitable closure methods. Several numerical examples illustrate the effectiveness of such a hierarchical approach at the various scales.