# Controllability and optimal control of the transport equation with a localized vector field

arXiv: https://arxiv.org/abs/1702.07272 · HTML: https://mlsanity.com/paper/1702.07272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2017.

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

- [Interplay between depth and width for interpolation in neural ODEs](https://mlsanity.com/paper/2401.09902/) (2024)

## Abstract (arXiv)

We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set ω. We prove that, for each initial and final configuration, one can steer one to another with such class of controls only if the uncontrolled dynamics allows to cross the control set ω. We also prove a minimal time result for such systems. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in ω to feed the desired final configuration.