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arXiv · 2611.02293

Small-time controllability of affine systems and quadratic Lie brackets

Karine Beauchard·Eugenio Pozzoli
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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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Karine Beauchard, Eugenio Pozzoli. 2026-11-01. Small-time controllability of affine systems and quadratic Lie brackets. https://arxiv.org/abs/2611.02293

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