On finite-dimensional parametrizations of attainability sets
type: Item
instance of: scholarly article
title: On finite-dimensional parametrizations of attainability sets
zbMATH Open document ID: 0885.93008
DOI: 10.1016/0096-3003(96)00004-5
author: Valerii I. Heymann
author: A. V. Kryazhimskij
published in: Applied Mathematics and Computation
publication date: 1996-11-12T00:00:00Z
review text: Nonlinear finite-dimensional, continuous-time control systems are considered. Under the assumption that there is only a scalar control function, a formal definition of the attainable sets is given. Next, a method of finite-dimensional parametrization of the attainable sets is proposed. It should be stressed that the parametrization is universal, i.e., the same for all attainable sets of a fixed dimension. Moreover, it is shown, that an upper estimate on the number of switchings sufficient to bring the control system to an arbitrary reachable state at a prescribed time is finite and depends on the dimensionality of the state space. Several remarks and comments on the properties of the attainable sets are also given. Similar problems have been considered in the paper [\textit{A. A. Agrachev} and \textit{S. A. Vakhrameev}, Sov. Math., Dokl. 30, 620-624 (1984); translation from Dokl. Akad. Nauk SSSR 279, No. 2, 265-269 (1984)].
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C99
zbMATH DE Number: 932142
zbMATH Keywords: nonlinear
zbMATH Keywords: parametrization
zbMATH Keywords: attainable sets
zbMATH Keywords: switchings
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
full work available at URL: 0096-3003(96)00004-5
OpenAlex ID: W1913355727
cites work: System Theory on Group Manifolds and Coset Spaces
cites work: Bilinear control processes. With applications to engineering, ecology, and medicine
cites work: Finite and infinite dimensional bilinear realizations
description: scientific article; zbMATH DE number 932142