# A collisionless singular Cucker-Smale model with decentralized formation control

arXiv: https://arxiv.org/abs/1807.05177 · HTML: https://mlsanity.com/paper/1807.05177/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [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)
- [Learning Decentralized Swarms Using Rotation Equivariant Graph Neural Networks](https://mlsanity.com/paper/2502.17612/) (2025)

## Abstract (arXiv)

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance between each agent and pre-assigned subset of neighbours. Such a design represents a multidimensional extension of existing control laws for 1d platoon formation control. For the proposed controller we study consensus emergence, collision-avoidance and formation control features in terms of energy estimates for the closed-loop system. Numerical experiments in 1, 2 and 3 dimensions assess the different features of the proposed design.