Ensemble controllability by lie algebraic methods

Andrei Agrachev, Yuliy Baryshnikov, Andrey Sarychev

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in R3, and provide a variant of Rashevsky−Chow theorem for approximate controllability of control-linear ensembles.

Original languageEnglish
Pages (from-to)921-938
Number of pages18
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume22
Issue number4
DOIs
Publication statusPublished - Oct 1 2016

Fingerprint

Algebraic Methods
Controllability
Approximate Controllability
Ensemble
Nonlinear control systems
Genericity
Exact Controllability
Nonlinear Control Systems
Linear Control
Sufficient
Theorem
Model

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

Cite this

Ensemble controllability by lie algebraic methods. / Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey.

In: ESAIM - Control, Optimisation and Calculus of Variations, Vol. 22, No. 4, 01.10.2016, p. 921-938.

Research output: Contribution to journalArticle

Agrachev, Andrei ; Baryshnikov, Yuliy ; Sarychev, Andrey. / Ensemble controllability by lie algebraic methods. In: ESAIM - Control, Optimisation and Calculus of Variations. 2016 ; Vol. 22, No. 4. pp. 921-938.
@article{3d3a0c207a5a432fa8419066c8792c1d,
title = "Ensemble controllability by lie algebraic methods",
abstract = "We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in R3, and provide a variant of Rashevsky−Chow theorem for approximate controllability of control-linear ensembles.",
author = "Andrei Agrachev and Yuliy Baryshnikov and Andrey Sarychev",
year = "2016",
month = "10",
day = "1",
doi = "10.1051/cocv/2016029",
language = "English",
volume = "22",
pages = "921--938",
journal = "ESAIM - Control, Optimisation and Calculus of Variations",
issn = "1292-8119",
publisher = "EDP Sciences",
number = "4",

}

TY - JOUR

T1 - Ensemble controllability by lie algebraic methods

AU - Agrachev, Andrei

AU - Baryshnikov, Yuliy

AU - Sarychev, Andrey

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in R3, and provide a variant of Rashevsky−Chow theorem for approximate controllability of control-linear ensembles.

AB - We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in R3, and provide a variant of Rashevsky−Chow theorem for approximate controllability of control-linear ensembles.

UR - http://www.scopus.com/inward/record.url?scp=85041469391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041469391&partnerID=8YFLogxK

U2 - 10.1051/cocv/2016029

DO - 10.1051/cocv/2016029

M3 - Article

AN - SCOPUS:85041469391

VL - 22

SP - 921

EP - 938

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 4

ER -