# Asymptotic behavior and control of a "guidance by repulsion" model

arXiv: https://arxiv.org/abs/1911.01133 · HTML: https://mlsanity.com/paper/1911.01133/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2019.

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

- [Stabilizing Backpropagation Through Time to Learn Complex Physics](https://mlsanity.com/paper/2405.02041/) (2024)
- [Hierarchical Policy-Gradient Reinforcement Learning for Multi-Agent Shepherding Control of Non-Cohesive Targets](https://mlsanity.com/paper/2504.02479/) (2025)

## Abstract (arXiv)

We model and analyze a herding problem, where the drivers try to steer the evaders' trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [Escobedo, R., Iba~nez, A. and Zuazua, E. COMMUN NONLINEAR SCI 39 (2016) 58-72], where the authors answer how to control the evaders' positions and what is the optimal maneuver of the drivers. First, we obtain the well-posedness and the long-time behavior of the one-driver and one-evader model, assuming of the same friction coefficients. In this case, the exact controllability is proved in a long enough time horizon. We extend the model to the multi-driver and multi-evader case, and develop numerical simulations to systematically explore the nature of controlled dynamics in various scenarios. The optimal strategies turn out to share a common pattern to the one-driver and one-evader case: the drivers rapidly occupy the position behind the target, and want to pursuit evaders in a straight line for most of the time. Inspired by this, we build a feedback strategy which stabilizes the direction of evaders.