Finite determination of accessibility and singular points of nonlinear systems: An algebraic approach

Mohammad Amin Sarafrazi , Ülle Kotta , Zbigniew Bartosiewicz

Abstract

Exploiting tools from algebraic geometry, the problem of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The results are constructive, and algorithms are given to find the maximum depth of Lie brackets necessary for deciding accessibility/strong accessibility of the system at any point, called here accessibility/strong accessibility index of the system, and known as the degree of non-holonomy in the literature. Alternatively, upper bounds on the accessibility/strong accessibility index are obtained, which can be computed easier. In each approach, the entire set of accessibility/strong accessibility singular points are obtained, as a limiting algebraic set of a strictly increasing chain of ideals, that stabilizes in finite time. Several examples demonstrate the applicability of the results using computer algebra tools.
Author Mohammad Amin Sarafrazi
Mohammad Amin Sarafrazi,,
-
, Ülle Kotta
Ülle Kotta,,
-
, Zbigniew Bartosiewicz (FCS / DM)
Zbigniew Bartosiewicz,,
- Department of Mathematics
Journal seriesSystems & Control Letters, [Systems and Control Letters], ISSN 0167-6911, e-ISSN 1872-7956, (N/A 100 pkt)
Issue year2020
Vol136
Pages1-7
Article number104600
Keywords in EnglishAccessibility, Singular points, Nonlinear systems, Algebraic approaches, Degree of non-holonomy
ASJC Classification1700 General Computer Science; 2207 Control and Systems Engineering; 2208 Electrical and Electronic Engineering; 2210 Mechanical Engineering
DOIDOI:10.1016/j.sysconle.2019.104600
Internal identifierROC 19-20
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 26-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 2.087; WoS Impact Factor: 2018 = 2.624 (2) - 2018=3.117 (5)
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?