Work

Factor-parity Hall sets and controllability

Year: 2026

Type: preprint

Abstract: We introduce a class of Hall sets, which we call factor-parity Hall sets, whose elements split into good and bad brackets. We prove that the good brackets can be steered simultaneously and arbitrarily in small time, which yields sufficient conditions for the small-time local controllability of control-affine systems. This positive result draws on constructions of Kawski, Agrachev-Gamkrelidze and Krastanov. Conversely, we prove that each bad bracket generates an obstruction to controllability, hence a family of necessary conditions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.04056

Authors: Beauchard, Karine, Marbach, Frédéric

Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Fondation Simone et Cino Del Duca

OpenAlex ID: W7208730761

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