CONTROL SYSTEM DEPENDING ON A PARAMETER
A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2021-07-01
|
Series: | Ural Mathematical Journal |
Subjects: | |
Online Access: | https://umjuran.ru/index.php/umj/article/view/377 |
id |
doaj-d2431d43d3374fd7ad516b9d377386ff |
---|---|
record_format |
Article |
spelling |
doaj-d2431d43d3374fd7ad516b9d377386ff2021-08-02T14:22:35ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. Ural Mathematical Journal2414-39522021-07-017110.15826/umj.2021.1.011123CONTROL SYSTEM DEPENDING ON A PARAMETERVladimir N. Ushakov0Aleksandr A. Ershov1Andrey V. Ushakov2Oleg A. Kuvshinov3Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.https://umjuran.ru/index.php/umj/article/view/377control system, differential inclusion, reachable set, integral funnel, parameter dependence, approximation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Vladimir N. Ushakov Aleksandr A. Ershov Andrey V. Ushakov Oleg A. Kuvshinov |
spellingShingle |
Vladimir N. Ushakov Aleksandr A. Ershov Andrey V. Ushakov Oleg A. Kuvshinov CONTROL SYSTEM DEPENDING ON A PARAMETER Ural Mathematical Journal control system, differential inclusion, reachable set, integral funnel, parameter dependence, approximation |
author_facet |
Vladimir N. Ushakov Aleksandr A. Ershov Andrey V. Ushakov Oleg A. Kuvshinov |
author_sort |
Vladimir N. Ushakov |
title |
CONTROL SYSTEM DEPENDING ON A PARAMETER |
title_short |
CONTROL SYSTEM DEPENDING ON A PARAMETER |
title_full |
CONTROL SYSTEM DEPENDING ON A PARAMETER |
title_fullStr |
CONTROL SYSTEM DEPENDING ON A PARAMETER |
title_full_unstemmed |
CONTROL SYSTEM DEPENDING ON A PARAMETER |
title_sort |
control system depending on a parameter |
publisher |
Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
series |
Ural Mathematical Journal |
issn |
2414-3952 |
publishDate |
2021-07-01 |
description |
A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given. |
topic |
control system, differential inclusion, reachable set, integral funnel, parameter dependence, approximation |
url |
https://umjuran.ru/index.php/umj/article/view/377 |
work_keys_str_mv |
AT vladimirnushakov controlsystemdependingonaparameter AT aleksandraershov controlsystemdependingonaparameter AT andreyvushakov controlsystemdependingonaparameter AT olegakuvshinov controlsystemdependingonaparameter |
_version_ |
1721231269374722048 |