PreprintCC BY 4.0HAL
Small-time controllability of affine systems and quadratic Lie brackets
Abstract
We prove a new sufficient condition for small-time global exact controllability of finite-dimensional control-affine systems. It points out that, under a natural Lie algebra rank condition, quadratic Lie brackets are the only possible obstacles to controllability. This result extends to infinite-dimensional settings such as the global approximate controllability of diffeomorphisms. It also allows us to interpret recent results in PDE control theory.
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BibTeX
@misc{beauchard2026smalltime,
title = {{Small-time controllability of affine systems and quadratic Lie brackets}},
author = {Karine Beauchard and Eugenio Pozzoli},
howpublished = {HAL},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02293},
eprint = {2611.02293},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05847509v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Small-time controllability of affine systems and quadratic Lie brackets
AU - Karine Beauchard
AU - Eugenio Pozzoli
PY - 2026
DA - 2026/11/01
PB - HAL
DO - 10.48550/arxiv.2611.02293
UR - https://hal.science/hal-05847509v1
AB - We prove a new sufficient condition for small-time global exact controllability of finite-dimensional control-affine systems. It points out that, under a natural Lie algebra rank condition, quadratic Lie brackets are the only possible obstacles to controllability. This result extends to infinite-dimensional settings such as the global approximate controllability of diffeomorphisms. It also allows us to interpret recent results in PDE control theory.
ER -