The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems

We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differentia...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics & optimization 2023-06, Vol.87 (3), p.58, Article 58
Main Author: Tuffaha, Amjad
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Boundary control
Calculus of Variations and Optimal Control
Optimization
Control
Hilbert space
Integral equations
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Noise control
Numerical and Computational Physics
Operators (mathematics)
Optimal control
Optimization
Partial differential equations
Riccati equation
Simulation
Stochastic processes
Systems analysis
Systems Theory
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3
cites cdi_FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3
container_end_page
container_issue 3
container_start_page 58
container_title Applied mathematics & optimization
container_volume 87
creator Tuffaha, Amjad
description We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differential equation with noise in the control, and with a C 0 -semigroup driving the deterministic component of the dynamics, and unbounded control action satisfying a singular estimate. We derive the feedback relation for the optimal control in terms of the optimal state via an operator solving an Algebraic Riccati equation. We show that the algebraic Riccati equation is well posed and has a unique solution in an appropriate class. These systems are typically coupled systems of stochastic partial differential equations comprising both parabolic and hyperbolic components with point or boundary control.
doi_str_mv 10.1007/s00245-023-09969-1
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2797451027</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2797451027</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3</originalsourceid><addsrcrecordid>eNp9kEFLwzAUx4MoOKdfwFPAc_S9Jm0Wb1LUCcMpm-eQZqmrdk1NusO-va0VvHnJg_D7_3jvT8glwjUCyJsIkIiUQcIZKJUphkdkgoInDDLIjskEQKVMZJidkrMYP6DnecYn5HO9dXTVebs1sassXVSNM4G-7s0mmOFj2XbVztQ0900XfE1fgi9qt6O-ofOqLlzo6Ko11sVbOqhyEx31JX32DTONqQ-DY3WIndvFc3JSmjq6i985JW8P9-t8zhbLx6f8bsEsR9UxhIJLWaazRCiLUgCKUlgsRJFxAziz0qnSWjTKZoCQGuWKpH_QbtAWruBTcjV62-C_9i52-sPvQ79M1IlUUqQIieypZKRs8DEGV-o29JeGg0bQQ6l6LFX3TemfUjX2IT6GYg837y78qf9JfQOIKXod</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2797451027</pqid></control><display><type>article</type><title>The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems</title><source>Business Source Ultimate</source><source>ABI/INFORM Global</source><source>Springer Link</source><creator>Tuffaha, Amjad</creator><creatorcontrib>Tuffaha, Amjad</creatorcontrib><description>We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differential equation with noise in the control, and with a C 0 -semigroup driving the deterministic component of the dynamics, and unbounded control action satisfying a singular estimate. We derive the feedback relation for the optimal control in terms of the optimal state via an operator solving an Algebraic Riccati equation. We show that the algebraic Riccati equation is well posed and has a unique solution in an appropriate class. These systems are typically coupled systems of stochastic partial differential equations comprising both parabolic and hyperbolic components with point or boundary control.</description><identifier>ISSN: 0095-4616</identifier><identifier>EISSN: 1432-0606</identifier><identifier>DOI: 10.1007/s00245-023-09969-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Applied mathematics ; Boundary control ; Calculus of Variations and Optimal Control; Optimization ; Control ; Hilbert space ; Integral equations ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Noise control ; Numerical and Computational Physics ; Operators (mathematics) ; Optimal control ; Optimization ; Partial differential equations ; Riccati equation ; Simulation ; Stochastic processes ; Systems analysis ; Systems Theory ; Theoretical</subject><ispartof>Applied mathematics &amp; optimization, 2023-06, Vol.87 (3), p.58, Article 58</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3</citedby><cites>FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3</cites><orcidid>0000-0001-8468-0688</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2797451027/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2797451027?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,11688,27924,27925,36060,44363,74895</link.rule.ids></links><search><creatorcontrib>Tuffaha, Amjad</creatorcontrib><title>The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems</title><title>Applied mathematics &amp; optimization</title><addtitle>Appl Math Optim</addtitle><description>We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differential equation with noise in the control, and with a C 0 -semigroup driving the deterministic component of the dynamics, and unbounded control action satisfying a singular estimate. We derive the feedback relation for the optimal control in terms of the optimal state via an operator solving an Algebraic Riccati equation. We show that the algebraic Riccati equation is well posed and has a unique solution in an appropriate class. These systems are typically coupled systems of stochastic partial differential equations comprising both parabolic and hyperbolic components with point or boundary control.</description><subject>Algebra</subject><subject>Applied mathematics</subject><subject>Boundary control</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Hilbert space</subject><subject>Integral equations</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Noise control</subject><subject>Numerical and Computational Physics</subject><subject>Operators (mathematics)</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Partial differential equations</subject><subject>Riccati equation</subject><subject>Simulation</subject><subject>Stochastic processes</subject><subject>Systems analysis</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0095-4616</issn><issn>1432-0606</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>M0C</sourceid><recordid>eNp9kEFLwzAUx4MoOKdfwFPAc_S9Jm0Wb1LUCcMpm-eQZqmrdk1NusO-va0VvHnJg_D7_3jvT8glwjUCyJsIkIiUQcIZKJUphkdkgoInDDLIjskEQKVMZJidkrMYP6DnecYn5HO9dXTVebs1sassXVSNM4G-7s0mmOFj2XbVztQ0900XfE1fgi9qt6O-ofOqLlzo6Ko11sVbOqhyEx31JX32DTONqQ-DY3WIndvFc3JSmjq6i985JW8P9-t8zhbLx6f8bsEsR9UxhIJLWaazRCiLUgCKUlgsRJFxAziz0qnSWjTKZoCQGuWKpH_QbtAWruBTcjV62-C_9i52-sPvQ79M1IlUUqQIieypZKRs8DEGV-o29JeGg0bQQ6l6LFX3TemfUjX2IT6GYg837y78qf9JfQOIKXod</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Tuffaha, Amjad</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0001-8468-0688</orcidid></search><sort><creationdate>20230601</creationdate><title>The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems</title><author>Tuffaha, Amjad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Applied mathematics</topic><topic>Boundary control</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Hilbert space</topic><topic>Integral equations</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Noise control</topic><topic>Numerical and Computational Physics</topic><topic>Operators (mathematics)</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Partial differential equations</topic><topic>Riccati equation</topic><topic>Simulation</topic><topic>Stochastic processes</topic><topic>Systems analysis</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tuffaha, Amjad</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>ProQuest Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>ProQuest research library</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Applied mathematics &amp; optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tuffaha, Amjad</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems</atitle><jtitle>Applied mathematics &amp; optimization</jtitle><stitle>Appl Math Optim</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>87</volume><issue>3</issue><spage>58</spage><pages>58-</pages><artnum>58</artnum><issn>0095-4616</issn><eissn>1432-0606</eissn><abstract>We derive the algebraic Riccati equation associated with the infinite dimensional linear quadratic stochastic optimal control problem on an infinite horizon, for stochastic control systems with non-analytic dynamics. The linear system under consideration is modeled by a linear stochastic differential equation with noise in the control, and with a C 0 -semigroup driving the deterministic component of the dynamics, and unbounded control action satisfying a singular estimate. We derive the feedback relation for the optimal control in terms of the optimal state via an operator solving an Algebraic Riccati equation. We show that the algebraic Riccati equation is well posed and has a unique solution in an appropriate class. These systems are typically coupled systems of stochastic partial differential equations comprising both parabolic and hyperbolic components with point or boundary control.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00245-023-09969-1</doi><orcidid>https://orcid.org/0000-0001-8468-0688</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0095-4616
ispartof Applied mathematics & optimization, 2023-06, Vol.87 (3), p.58, Article 58
issn 0095-4616
1432-0606
language eng
recordid cdi_proquest_journals_2797451027
source Business Source Ultimate; ABI/INFORM Global; Springer Link
subjects Algebra
Applied mathematics
Boundary control
Calculus of Variations and Optimal Control
Optimization
Control
Hilbert space
Integral equations
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Noise control
Numerical and Computational Physics
Operators (mathematics)
Optimal control
Optimization
Partial differential equations
Riccati equation
Simulation
Stochastic processes
Systems analysis
Systems Theory
Theoretical
title The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T07%3A09%3A59IST&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=The%20Stochastic%20Linear%20Quadratic%20Optimal%20Control%20Problem%20on%20Hilbert%20Spaces:%20The%20Case%20of%20Non-analytic%20Systems&rft.jtitle=Applied%20mathematics%20&%20optimization&rft.au=Tuffaha,%20Amjad&rft.date=2023-06-01&rft.volume=87&rft.issue=3&rft.spage=58&rft.pages=58-&rft.artnum=58&rft.issn=0095-4616&rft.eissn=1432-0606&rft_id=info:doi/10.1007/s00245-023-09969-1&rft_dat=%3Cproquest_cross%3E2797451027%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-10b377f58249c174014f4c1b4b63a018c7e9fcc1a9c60105a9eb2a9e1cd1cbeb3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2797451027&rft_id=info:pmid/&rfr_iscdi=true