Control systems subordinated to a group action: Accessibility
type: Item
instance of: scholarly article
title: Control systems subordinated to a group action: Accessibility
zbMATH Open document ID: 0531.93008
DOI: 10.1016/0022-0396(81)90072-3
published in: Journal of Differential Equations
publication date: 1981-01-01T00:00:00Z
review text: Let M be an n-dimensional real \(C^{\infty}\) manifold; a polysystem on M is a family of \(C^{\infty}\) vector fields on M. Let G be a real connected Lie group which acts smoothly on M and let \(\Gamma\) be a subset of the Lie algebra of G. \(\Gamma\) defines a polysystem on M, the polysystem of the vector fields canonically induced by the elements of \(\Gamma\). Such a polysystem is called subordinated to a group action. A polysystem is transitive (controllable) on M if for each x, y belonging to M, there exists a trajectory of the polysystem which steers x to y. The authors give sufficient conditions for transitivity of a polysystem on GL(V) (V a finite dimensional vector space) associated to \(\Gamma =\{A+uB:\) \(u\in R\), A,\(B\in End(V)\}\).
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 3843578
zbMATH Keywords: bilinear systems
zbMATH Keywords: polysystem
zbMATH Keywords: transitivity
author: Velimir Jurdjevic
author: I. Kupka
reviewed by: Rosa Maria Bianchini
MaRDI profile type: Publication
full work available at URL: 0022-0396(81)90072-3
OpenAlex ID: W2038140295
cites work: Functional analysis and time optimal control
cites work: Control systems on semi-simple Lie groups and their homogeneous spaces
cites work: Controllability and stability
cites work: Controllability of nonlinear systems
description: scientific article; zbMATH DE number 3843578