# Ensemble controllability by Lie algebraic methods

arXiv: https://arxiv.org/abs/1603.07133 · HTML: https://mlsanity.com/paper/1603.07133/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2016.

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

- [Turnpike in optimal control of PDEs, ResNets, and beyond](https://mlsanity.com/paper/2202.04097/) (2022)
- [Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems](https://mlsanity.com/paper/2110.12393/) (2021)

## Abstract (arXiv)

We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in ℝ3, and provide a variant of Rashevsky-Chow theorem for approximate controllability of control-linear ensembles.