Controllability in codimension one
type: Item
instance of: scholarly article
title: Controllability in codimension one
zbMATH Open document ID: 0621.93008
DOI: 10.1016/0022-0396(87)90182-3
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: Let M be an n-dimensional connected analytic manifold. A nonlinear control system of the form \((*)\quad x'=X(x)+\sum^{s}_{i=1}u_ iX^ i(x),\) \(x\in M\) is said to have codimension one when the Lie algebra generated by the vector fields \(X^ 1,...,X^ s\) has dimension n-1 at every point of M. In this paper it is proved that some necessary conditions formerly obtained by the same author, plus some transversality conditions, turn out to be sufficient for local and global controllability of (*).
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 4008190
zbMATH Keywords: nonlinear control system
zbMATH Keywords: Lie algebra
zbMATH Keywords: transversality
zbMATH Keywords: local and global controllability
author: J. Basto-Gonçalves
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90182-3
OpenAlex ID: W2164213297
cites work: Global Controllability for Smooth Nonlinear Systems: A Geometric Approach
cites work: On the relationship between global and local controllability
cites work: Local controllability of nonlinear systems
cites work: A condition equivalent to global controllability in systems of vector fields
cites work: Q5734946
cites work: Local controllability and sufficient conditions in singular problems
cites work: Controlled stability
cites work: On Local Controllability
cites work: Control systems which generate decomposable Lie algebras
cites work: Differential Topology
cites work: Controllability of general nonlinear systems
cites work: Global controllability of nonlinear systems in two dimensions
cites work: &lt;tex&gt;n&lt;/tex&gt;-Dimensional controllability with&lt;tex&gt;(n-1)&lt;/tex&gt;controls
cites work: A Sufficient Condition for Local Controllability
cites work: Lie Brackets and Local Controllability: A Sufficient Condition for Scalar-Input Systems
cites work: Controllability of nonlinear systems
description: scientific article; zbMATH DE number 4008190