On a Differential Game in a Stochastic System

We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class subscript C...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2020-08, Vol.309 (Suppl 1), p.S185-S198
Hauptverfasser: Vlasenko, L. A., Rutkas, A. G., Chikrii, A. A.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page S198
container_issue Suppl 1
container_start_page S185
container_title Proceedings of the Steklov Institute of Mathematics
container_volume 309
creator Vlasenko, L. A.
Rutkas, A. G.
Chikrii, A. A.
description We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class subscript C 0 ). Solutions of the equation are represented by a stochastic variation of constants formula. Using constraints on the support functionals of sets defined by the behavior of the pursuer and the evader, we obtain conditions for the approach of the system state to a cylindrical terminal set. The results are illustrated with a model example of a simple motion in a Hilbert space with random perturbations. Applications to distributed systems described by stochastic partial differential equations are considered. By taking into account a random external influence, we consider the heat propagation process with controlled distributed heat sources and sinks.
doi_str_mv 10.1134/S0081543820040203
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2437883779</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2437883779</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-fb35b0ada7f331f5e02f30f13d35e65185441404767e82a81e55866d6cdef0c63</originalsourceid><addsrcrecordid>eNp1kE9Lw0AQxRdRsFY_gLeA5-hMZv_1KFVbodBD9By2yaymNEndTQ_99iZU8CCeBt77vTfwhLhFuEck-ZADWFSSbAYgIQM6ExNUhKnVoM7FZLTT0b8UVzFuB0gZOZuIdN0mLnmqvefAbV-7XbJwDSf1KOd9V3662Ndlkh9jz821uPBuF_nm507F-8vz23yZrtaL1_njKi0JdZ_6DakNuMoZT4ReMWSewCNVpFgrtEpKlCCNNmwzZ5GVslpXuqzYQ6lpKu5OvfvQfR049sW2O4R2eFlkkoy1ZMxsoPBElaGLMbAv9qFuXDgWCMW4SvFnlSGTnTJxYNsPDr_N_4e-Ac8yYIE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2437883779</pqid></control><display><type>article</type><title>On a Differential Game in a Stochastic System</title><source>SpringerNature Journals</source><creator>Vlasenko, L. A. ; Rutkas, A. G. ; Chikrii, A. A.</creator><creatorcontrib>Vlasenko, L. A. ; Rutkas, A. G. ; Chikrii, A. A.</creatorcontrib><description>We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class subscript C 0 ). Solutions of the equation are represented by a stochastic variation of constants formula. Using constraints on the support functionals of sets defined by the behavior of the pursuer and the evader, we obtain conditions for the approach of the system state to a cylindrical terminal set. The results are illustrated with a model example of a simple motion in a Hilbert space with random perturbations. Applications to distributed systems described by stochastic partial differential equations are considered. By taking into account a random external influence, we consider the heat propagation process with controlled distributed heat sources and sinks.</description><identifier>ISSN: 0081-5438</identifier><identifier>EISSN: 1531-8605</identifier><identifier>DOI: 10.1134/S0081543820040203</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Computer networks ; Differential games ; Heat sinks ; Heat sources ; Hilbert space ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Partial differential equations ; Stochastic systems</subject><ispartof>Proceedings of the Steklov Institute of Mathematics, 2020-08, Vol.309 (Suppl 1), p.S185-S198</ispartof><rights>Pleiades Publishing, Ltd. 2020</rights><rights>Pleiades Publishing, Ltd. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-fb35b0ada7f331f5e02f30f13d35e65185441404767e82a81e55866d6cdef0c63</citedby><cites>FETCH-LOGICAL-c316t-fb35b0ada7f331f5e02f30f13d35e65185441404767e82a81e55866d6cdef0c63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0081543820040203$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0081543820040203$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Vlasenko, L. A.</creatorcontrib><creatorcontrib>Rutkas, A. G.</creatorcontrib><creatorcontrib>Chikrii, A. A.</creatorcontrib><title>On a Differential Game in a Stochastic System</title><title>Proceedings of the Steklov Institute of Mathematics</title><addtitle>Proc. Steklov Inst. Math</addtitle><description>We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class subscript C 0 ). Solutions of the equation are represented by a stochastic variation of constants formula. Using constraints on the support functionals of sets defined by the behavior of the pursuer and the evader, we obtain conditions for the approach of the system state to a cylindrical terminal set. The results are illustrated with a model example of a simple motion in a Hilbert space with random perturbations. Applications to distributed systems described by stochastic partial differential equations are considered. By taking into account a random external influence, we consider the heat propagation process with controlled distributed heat sources and sinks.</description><subject>Computer networks</subject><subject>Differential games</subject><subject>Heat sinks</subject><subject>Heat sources</subject><subject>Hilbert space</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Partial differential equations</subject><subject>Stochastic systems</subject><issn>0081-5438</issn><issn>1531-8605</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kE9Lw0AQxRdRsFY_gLeA5-hMZv_1KFVbodBD9By2yaymNEndTQ_99iZU8CCeBt77vTfwhLhFuEck-ZADWFSSbAYgIQM6ExNUhKnVoM7FZLTT0b8UVzFuB0gZOZuIdN0mLnmqvefAbV-7XbJwDSf1KOd9V3662Ndlkh9jz821uPBuF_nm507F-8vz23yZrtaL1_njKi0JdZ_6DakNuMoZT4ReMWSewCNVpFgrtEpKlCCNNmwzZ5GVslpXuqzYQ6lpKu5OvfvQfR049sW2O4R2eFlkkoy1ZMxsoPBElaGLMbAv9qFuXDgWCMW4SvFnlSGTnTJxYNsPDr_N_4e-Ac8yYIE</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Vlasenko, L. A.</creator><creator>Rutkas, A. G.</creator><creator>Chikrii, A. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200801</creationdate><title>On a Differential Game in a Stochastic System</title><author>Vlasenko, L. A. ; Rutkas, A. G. ; Chikrii, A. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-fb35b0ada7f331f5e02f30f13d35e65185441404767e82a81e55866d6cdef0c63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer networks</topic><topic>Differential games</topic><topic>Heat sinks</topic><topic>Heat sources</topic><topic>Hilbert space</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Partial differential equations</topic><topic>Stochastic systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vlasenko, L. A.</creatorcontrib><creatorcontrib>Rutkas, A. G.</creatorcontrib><creatorcontrib>Chikrii, A. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vlasenko, L. A.</au><au>Rutkas, A. G.</au><au>Chikrii, A. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a Differential Game in a Stochastic System</atitle><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle><stitle>Proc. Steklov Inst. Math</stitle><date>2020-08-01</date><risdate>2020</risdate><volume>309</volume><issue>Suppl 1</issue><spage>S185</spage><epage>S198</epage><pages>S185-S198</pages><issn>0081-5438</issn><eissn>1531-8605</eissn><abstract>We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class subscript C 0 ). Solutions of the equation are represented by a stochastic variation of constants formula. Using constraints on the support functionals of sets defined by the behavior of the pursuer and the evader, we obtain conditions for the approach of the system state to a cylindrical terminal set. The results are illustrated with a model example of a simple motion in a Hilbert space with random perturbations. Applications to distributed systems described by stochastic partial differential equations are considered. By taking into account a random external influence, we consider the heat propagation process with controlled distributed heat sources and sinks.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0081543820040203</doi></addata></record>
fulltext fulltext
identifier ISSN: 0081-5438
ispartof Proceedings of the Steklov Institute of Mathematics, 2020-08, Vol.309 (Suppl 1), p.S185-S198
issn 0081-5438
1531-8605
language eng
recordid cdi_proquest_journals_2437883779
source SpringerNature Journals
subjects Computer networks
Differential games
Heat sinks
Heat sources
Hilbert space
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
Stochastic systems
title On a Differential Game in a Stochastic System
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T14%3A49%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20Differential%20Game%20in%20a%20Stochastic%20System&rft.jtitle=Proceedings%20of%20the%20Steklov%20Institute%20of%20Mathematics&rft.au=Vlasenko,%20L.%20A.&rft.date=2020-08-01&rft.volume=309&rft.issue=Suppl%201&rft.spage=S185&rft.epage=S198&rft.pages=S185-S198&rft.issn=0081-5438&rft.eissn=1531-8605&rft_id=info:doi/10.1134/S0081543820040203&rft_dat=%3Cproquest_cross%3E2437883779%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2437883779&rft_id=info:pmid/&rfr_iscdi=true