Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabil...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:International journal of robust and nonlinear control 2001-03, Vol.11 (3), p.253-265
1. Verfasser: Polushin, Ilya G.
Format: Artikel
Sprache:eng
Schlagworte:
disturbances
Hamiltonian systems
oscillations control
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 265
container_issue 3
container_start_page 253
container_title International journal of robust and nonlinear control
container_volume 11
creator Polushin, Ilya G.
description The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)‐definiteness of time derivative of V. Copyright © 2001 John Wiley & Sons, Ltd.
doi_str_mv 10.1002/rnc.569
format Article
fullrecord <record><control><sourceid>istex_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_rnc_569</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ark_67375_WNG_SQKQ7KKP_R</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2979-2d5ac4373288bb62511b05c0667ccbbad45a15a5cf795a2cf8ff5d97f2a264fd3</originalsourceid><addsrcrecordid>eNp1kFFLwzAQx4MoOKf4FfLmg3QmadM0jzJ0k43pNsUnCWnaSLRLR5Kp9dObUfHNp7v734-D-wFwjtEII0SunFUjmvMDMMCI8wSTlB_u-4wnBSfpMTjx_g2huCPZALysgyxNY75lMK2FrYbGfkhnpA0wtM7EEU7lxjShtTGEvvOh3ni4s1Xt4LZ23sTAhqaDUgVjX2EVg50rpVW1PwVHWja-PvutQ_B0e_M4nibz-8nd-HqeKMIZT0hFpcpSlpKiKMucUIxLRBXKc6ZUWcoqoxJTSZVmnEqidKE1rTjTRJI801U6BBf9XeVa712txdaZjXSdwEjsrYhoRUQrkbzsyU_T1N1_mFgtxj2d9PT-ya8_Wrp3kbOUUfG8mIj1crZks9mDWKU_LyR1Wg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances</title><source>Wiley Online Library - AutoHoldings Journals</source><creator>Polushin, Ilya G.</creator><creatorcontrib>Polushin, Ilya G.</creatorcontrib><description>The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)‐definiteness of time derivative of V. Copyright © 2001 John Wiley &amp; Sons, Ltd.</description><identifier>ISSN: 1049-8923</identifier><identifier>EISSN: 1099-1239</identifier><identifier>DOI: 10.1002/rnc.569</identifier><language>eng</language><publisher>Chichester, UK: John Wiley &amp; Sons, Ltd</publisher><subject>disturbances ; Hamiltonian systems ; oscillations control</subject><ispartof>International journal of robust and nonlinear control, 2001-03, Vol.11 (3), p.253-265</ispartof><rights>Copyright © 2001 John Wiley &amp; Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2979-2d5ac4373288bb62511b05c0667ccbbad45a15a5cf795a2cf8ff5d97f2a264fd3</citedby><cites>FETCH-LOGICAL-c2979-2d5ac4373288bb62511b05c0667ccbbad45a15a5cf795a2cf8ff5d97f2a264fd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Frnc.569$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Frnc.569$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Polushin, Ilya G.</creatorcontrib><title>Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances</title><title>International journal of robust and nonlinear control</title><addtitle>Int. J. Robust Nonlinear Control</addtitle><description>The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)‐definiteness of time derivative of V. Copyright © 2001 John Wiley &amp; Sons, Ltd.</description><subject>disturbances</subject><subject>Hamiltonian systems</subject><subject>oscillations control</subject><issn>1049-8923</issn><issn>1099-1239</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNp1kFFLwzAQx4MoOKf4FfLmg3QmadM0jzJ0k43pNsUnCWnaSLRLR5Kp9dObUfHNp7v734-D-wFwjtEII0SunFUjmvMDMMCI8wSTlB_u-4wnBSfpMTjx_g2huCPZALysgyxNY75lMK2FrYbGfkhnpA0wtM7EEU7lxjShtTGEvvOh3ni4s1Xt4LZ23sTAhqaDUgVjX2EVg50rpVW1PwVHWja-PvutQ_B0e_M4nibz-8nd-HqeKMIZT0hFpcpSlpKiKMucUIxLRBXKc6ZUWcoqoxJTSZVmnEqidKE1rTjTRJI801U6BBf9XeVa712txdaZjXSdwEjsrYhoRUQrkbzsyU_T1N1_mFgtxj2d9PT-ya8_Wrp3kbOUUfG8mIj1crZks9mDWKU_LyR1Wg</recordid><startdate>200103</startdate><enddate>200103</enddate><creator>Polushin, Ilya G.</creator><general>John Wiley &amp; Sons, Ltd</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200103</creationdate><title>Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances</title><author>Polushin, Ilya G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2979-2d5ac4373288bb62511b05c0667ccbbad45a15a5cf795a2cf8ff5d97f2a264fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>disturbances</topic><topic>Hamiltonian systems</topic><topic>oscillations control</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Polushin, Ilya G.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>International journal of robust and nonlinear control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Polushin, Ilya G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances</atitle><jtitle>International journal of robust and nonlinear control</jtitle><addtitle>Int. J. Robust Nonlinear Control</addtitle><date>2001-03</date><risdate>2001</risdate><volume>11</volume><issue>3</issue><spage>253</spage><epage>265</epage><pages>253-265</pages><issn>1049-8923</issn><eissn>1099-1239</eissn><abstract>The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)‐definiteness of time derivative of V. Copyright © 2001 John Wiley &amp; Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley &amp; Sons, Ltd</pub><doi>10.1002/rnc.569</doi><tpages>13</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1049-8923
ispartof International journal of robust and nonlinear control, 2001-03, Vol.11 (3), p.253-265
issn 1049-8923
1099-1239
language eng
recordid cdi_crossref_primary_10_1002_rnc_569
source Wiley Online Library - AutoHoldings Journals
subjects disturbances
Hamiltonian systems
oscillations control
title Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T13%3A44%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-istex_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stabilization%20of%20invariant%20tori%20in%20Hamiltonian%20systems%20under%20persistently%20acting%20disturbances&rft.jtitle=International%20journal%20of%20robust%20and%20nonlinear%20control&rft.au=Polushin,%20Ilya%20G.&rft.date=2001-03&rft.volume=11&rft.issue=3&rft.spage=253&rft.epage=265&rft.pages=253-265&rft.issn=1049-8923&rft.eissn=1099-1239&rft_id=info:doi/10.1002/rnc.569&rft_dat=%3Cistex_cross%3Eark_67375_WNG_SQKQ7KKP_R%3C/istex_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true