A condition equivalent to global controllability in systems of vector fields
type: Item
instance of: scholarly article
title: A condition equivalent to global controllability in systems of vector fields
zbMATH Open document ID: 0583.58028
DOI: 10.1016/0022-0396(85)90108-1
published in: Journal of Differential Equations
publication date: 1985-01-01T00:00:00Z
review text: Let S be a family of \(C^ 1\) vector fields on a finite-dimensional differentiable manifold M of class \(C^ k\) with \(k\geq 2\). Let A(x,S) be the set of all points in M that are reachable from x via a finite number of integral curves of vector fields from S. The family S is said to be globally controllable if \(A(x,S)=M\) for every \(x\in M\). When M is compact, a theorem of \textit{I. Kupka} and \textit{G. Sallet} [ibid. 47, 462- 470 (1983; Zbl 0527.93029)] states that S is globally controllable if and only if S has property (P), i.e. \(x\in int A(x,S)\) for every \(x\in M\). The author shows that this equivalence continues to hold when M is noncompact.
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 3934083
zbMATH Keywords: reachable sets
zbMATH Keywords: controllability
zbMATH Keywords: \(C^ 1\) vector fields
author: Kevin A. Grasse
reviewed by: Mihai Anastasiei
MaRDI profile type: Publication
full work available at URL: 0022-0396(85)90108-1
OpenAlex ID: W2072688453
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description: scientific article; zbMATH DE number 3934083