Adaptive identification of linear infinite-dimensional systems
We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (...
Uložené v:
| Vydané v: | International journal of control Ročník 98; číslo 3; s. 593 - 608 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Abingdon
Taylor & Francis
04.03.2025
Taylor & Francis Ltd |
| Predmet: | |
| ISSN: | 0020-7179, 1366-5820 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an adaptive update law (a differential equation in time) driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown linearly-varying (in space) coefficient. |
|---|---|
| AbstractList | We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an adaptive update law (a differential equation in time) driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown linearly-varying (in space) coefficient. |
| Author | Natarajan, Vivek Chattopadhyay, Sudipta Sukumar, Srikant |
| Author_xml | – sequence: 1 givenname: Sudipta surname: Chattopadhyay fullname: Chattopadhyay, Sudipta organization: Indian Institute of Technology Bombay – sequence: 2 givenname: Srikant surname: Sukumar fullname: Sukumar, Srikant organization: Indian Institute of Technology Bombay – sequence: 3 givenname: Vivek surname: Natarajan fullname: Natarajan, Vivek email: vivek.natarajan@iitb.ac.in organization: Indian Institute of Technology Bombay |
| BookMark | eNp9kE9LAzEQxYNUsK1-BGHB89ZJsrvZvYil-A8KXvQc0uwEUrZJTVKl394srVdPc5jfe_PmzcjEeYeE3FJYUGjhHoCBoKJbMGDVgvGaC04vyJTypinrlsGETEemHKErMotxC0B53dIpeVj2ap_sNxa2R5essVol613hTTFYhyoU1hnrbMKytzt0MS_VUMRjTLiL1-TSqCHizXnOyefz08fqtVy_v7ytlutSs7ZJJdMb0bFOK1EJaja96DVw6FC3HQBUghuhcyKhFMcKYFPpCpVgiJVqdJvZObk7-e6D_zpgTHLrDyEHiZLT_G1TU04zVZ8oHXyMAY3cB7tT4SgpyLEq-VeVHKuS56qy7vGky6_6sFM_Pgy9TOo4-GCCctqOZ_61-AW3W3F2 |
| Cites_doi | 10.4310/MAA.1999.v6.n4.a9 10.1109/TAC.2019.2893973 10.1080/00207171003586914 10.1016/j.automatica.2007.03.018 10.1109/CDC40024.2019.9030098 10.3166/ejc.8.165-175 10.1016/j.jprocont.2010.07.005 10.1109/TCST.2012.2204751 10.1088/0266-5611/10/2/006 10.1109/TAC.2017.2700387 10.1109/CDC40024.2019.9029327 10.1016/j.sysconle.2014.01.005 10.1007/s00498-003-0128-6 10.1016/j.apnum.2019.09.013 10.1109/CDC.2005.1582999 10.1109/9.284907 10.1016/0005-1098(94)90006-X 10.1088/0266-5611/26/3/035004 10.1137/S0363012900368636 10.1109/9.839944 10.1115/1.4024801 10.1088/0266-5611/32/4/045006 10.1109/CDC42340.2020.9303749 10.1137/0322043 10.1137/S0363012994270928 10.3182/20120711-3-BE-2027.00076 10.1109/TAC.2016.2643442 10.1515/9781400835362 10.1007/978-1-4612-5561-1 10.1080/00207179.2016.1266513 10.1051/cocv:1998105 10.1109/MED.2008.4602008 |
| ContentType | Journal Article |
| Copyright | 2024 Informa UK Limited, trading as Taylor & Francis Group 2024 2024 Informa UK Limited, trading as Taylor & Francis Group |
| Copyright_xml | – notice: 2024 Informa UK Limited, trading as Taylor & Francis Group 2024 – notice: 2024 Informa UK Limited, trading as Taylor & Francis Group |
| DBID | AAYXX CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D |
| DOI | 10.1080/00207179.2024.2353731 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1366-5820 |
| EndPage | 608 |
| ExternalDocumentID | 10_1080_00207179_2024_2353731 2353731 |
| Genre | Research Article |
| GrantInformation_xml | – fundername: Science and Engineering Research Board, DST India grantid: ECR/2017/002583 |
| GroupedDBID | -~X .7F .QJ 0BK 0R~ 29J 2DF 30N 4.4 5GY 5VS AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACBEA ACGEJ ACGFO ACGFS ACIWK ACTIO ADCVX ADGTB ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFKVX AFRVT AGDLA AGMYJ AHDZW AIJEM AIYEW AJWEG AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AMVHM AQRUH AQTUD AVBZW AWYRJ BLEHA CCCUG CE4 CS3 DGEBU DKSSO DU5 EBS E~A E~B F5P GTTXZ H13 HF~ HZ~ H~P IPNFZ J.P KYCEM LJTGL M4Z NA5 NX~ O9- P2P RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEN TFL TFT TFW TN5 TNC TTHFI TUROJ TWF UT5 UU3 ZGOLN ~S~ AAYXX CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c286t-2cb7929ca7471fbd7dc0309ec89000473f7c0137aa3e400b4c4ea72ee4a6c8c03 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001255531600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-7179 |
| IngestDate | Wed Aug 13 11:10:25 EDT 2025 Sat Nov 29 08:12:55 EST 2025 Mon Oct 20 23:48:05 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c286t-2cb7929ca7471fbd7dc0309ec89000473f7c0137aa3e400b4c4ea72ee4a6c8c03 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3173165131 |
| PQPubID | 176145 |
| PageCount | 16 |
| ParticipantIDs | proquest_journals_3173165131 crossref_primary_10_1080_00207179_2024_2353731 informaworld_taylorfrancis_310_1080_00207179_2024_2353731 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-04 |
| PublicationDateYYYYMMDD | 2025-03-04 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-04 day: 04 |
| PublicationDecade | 2020 |
| PublicationPlace | Abingdon |
| PublicationPlace_xml | – name: Abingdon |
| PublicationTitle | International journal of control |
| PublicationYear | 2025 |
| Publisher | Taylor & Francis Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Ltd |
| References | e_1_3_2_27_1 e_1_3_2_28_1 e_1_3_2_29_1 Ioannou P. A. (e_1_3_2_17_1) 2012 e_1_3_2_20_1 e_1_3_2_21_1 e_1_3_2_22_1 e_1_3_2_23_1 Curtain R. F. (e_1_3_2_11_1) 2003; 13 e_1_3_2_25_1 e_1_3_2_26_1 Morris K. A. (e_1_3_2_24_1) 1994; 4 e_1_3_2_16_1 e_1_3_2_9_1 e_1_3_2_8_1 e_1_3_2_18_1 e_1_3_2_7_1 e_1_3_2_19_1 e_1_3_2_2_1 e_1_3_2_31_1 e_1_3_2_30_1 e_1_3_2_10_1 e_1_3_2_33_1 e_1_3_2_32_1 e_1_3_2_6_1 e_1_3_2_12_1 e_1_3_2_35_1 e_1_3_2_5_1 e_1_3_2_13_1 e_1_3_2_34_1 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_3_1 e_1_3_2_15_1 e_1_3_2_36_1 |
| References_xml | – ident: e_1_3_2_34_1 doi: 10.4310/MAA.1999.v6.n4.a9 – ident: e_1_3_2_20_1 doi: 10.1109/TAC.2019.2893973 – ident: e_1_3_2_36_1 doi: 10.1080/00207171003586914 – ident: e_1_3_2_15_1 doi: 10.1016/j.automatica.2007.03.018 – ident: e_1_3_2_27_1 doi: 10.1109/CDC40024.2019.9030098 – ident: e_1_3_2_3_1 doi: 10.3166/ejc.8.165-175 – ident: e_1_3_2_23_1 doi: 10.1016/j.jprocont.2010.07.005 – ident: e_1_3_2_22_1 doi: 10.1109/TCST.2012.2204751 – ident: e_1_3_2_13_1 doi: 10.1088/0266-5611/10/2/006 – ident: e_1_3_2_2_1 doi: 10.1109/TAC.2017.2700387 – ident: e_1_3_2_18_1 doi: 10.1109/CDC40024.2019.9029327 – volume: 13 start-page: 441 year: 2003 ident: e_1_3_2_11_1 article-title: Adaptive compensators for perturbed positive real infinite-dimensional systems publication-title: International Journal of Applied Mathematics and Computer Science – ident: e_1_3_2_26_1 doi: 10.1016/j.sysconle.2014.01.005 – ident: e_1_3_2_9_1 doi: 10.1007/s00498-003-0128-6 – ident: e_1_3_2_19_1 doi: 10.1016/j.apnum.2019.09.013 – ident: e_1_3_2_29_1 doi: 10.1109/CDC.2005.1582999 – ident: e_1_3_2_12_1 doi: 10.1109/9.284907 – ident: e_1_3_2_16_1 doi: 10.1016/0005-1098(94)90006-X – ident: e_1_3_2_21_1 doi: 10.1088/0266-5611/26/3/035004 – ident: e_1_3_2_32_1 doi: 10.1137/S0363012900368636 – ident: e_1_3_2_30_1 doi: 10.1109/9.839944 – ident: e_1_3_2_25_1 doi: 10.1115/1.4024801 – ident: e_1_3_2_8_1 doi: 10.1088/0266-5611/32/4/045006 – ident: e_1_3_2_10_1 doi: 10.1109/CDC42340.2020.9303749 – ident: e_1_3_2_5_1 doi: 10.1137/0322043 – ident: e_1_3_2_6_1 doi: 10.1137/S0363012994270928 – ident: e_1_3_2_14_1 doi: 10.3182/20120711-3-BE-2027.00076 – ident: e_1_3_2_7_1 doi: 10.1109/TAC.2016.2643442 – volume: 4 start-page: 1 year: 1994 ident: e_1_3_2_24_1 article-title: Design of finite-dimensional controllers for infinite dimensional systems by approximation publication-title: Journal of Mathematical Systems, Estimation, and Control – ident: e_1_3_2_35_1 doi: 10.1515/9781400835362 – ident: e_1_3_2_31_1 doi: 10.1007/978-1-4612-5561-1 – volume-title: Robust adaptive control year: 2012 ident: e_1_3_2_17_1 – ident: e_1_3_2_28_1 doi: 10.1080/00207179.2016.1266513 – ident: e_1_3_2_4_1 doi: 10.1051/cocv:1998105 – ident: e_1_3_2_33_1 doi: 10.1109/MED.2008.4602008 |
| SSID | ssj0013581 |
| Score | 2.4375582 |
| Snippet | We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 593 |
| SubjectTerms | Adaptive algorithms Adaptive identification Estimates finite-dimensional approximations Infinite series irrational transfer functions Parameter identification Partial differential equations persistency of excitation Real time Scalars SISO (control systems) Thermodynamics Transfer functions Wave equations |
| Title | Adaptive identification of linear infinite-dimensional systems |
| URI | https://www.tandfonline.com/doi/abs/10.1080/00207179.2024.2353731 https://www.proquest.com/docview/3173165131 |
| Volume | 98 |
| WOSCitedRecordID | wos001255531600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAWR databaseName: Taylor and Francis Online Journals customDbUrl: eissn: 1366-5820 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0013581 issn: 0020-7179 databaseCode: TFW dateStart: 19650101 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxQADb0ShIA-sqZLYruMFqUJUDKhiKKJb5PghdUmrJvD78dkOtEKIAfb4oTuf7y6--z6EbrUmqYVSHW0ykVBqdSI0YQmzzDkfwdLKeBDXJz6dFvO5eI7VhE0sq4Qc2gagCH9Xg3HLqukq4qCDG7IQaDPJ6TAnjHDfSe1cP5jmbPL69Y7AisCZ55IkGNL18Pw0y5Z32sIu_XZXewc0OfyHrR-hgxh94nE4Lsdox9QnaH8Dk_AU3Y21XMEdiBc6VhJ55eGlxbCgXGO34QWEqokGaoAA64EDJHRzhl4mD7P7xySSLCQqL0ZtkquKuxBJSchObaW5VvDqYlQBdKKUE8sVwBJKSYyz94oqaiTPjaFypAr37Tnq1cvaXCDMU0VsUUkpqKU6JUWqFal0JiSTxJl3Hw074ZargKVRZp8QpUEwJQimjILpI7GpgrL1PzFsYBwpyS9jB52-ymiWMASIulhGsss_TH2F9nJgAYZKNDpAvXb9Zq7RrnpvF836xh_AD37W1q0 |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT8MwDLbQQAIOvCcGA3rg2qltkqW9IE2IaYix0xC7RWke0i7btBV-P3HTwiaEOMC9SSM7ju3E_j6AW61JZLFUR5s4Cym1Osw0YSGzzDmfjEW5KUFch3w0SieTbL0XBssqMYe2HiiiPKvRuPEyui6JwxZuTEOwzyShnYQwwrGVeps5X4v4-eP-69dLAks9a55Lk3BM3cXz0zQb_mkDvfTbaV26oP7hfyz-CA6qADTo-R1zDFtmdgL7a7CEp3DX03KBx2Aw1VUxUam_YG4D_KNcBm7FU4xWQ43sAB7ZI_Co0KszeOk_jO8HYcWzEKok7RZhonLuoiQlMUG1ueZa4cOLUSkyilJOLFeITCglMc7kc6qokTwxhsquSt23TWjM5jNzDgGPFLFpLmVGLdURSSOtSK7jTDJJnIW3oFNLVyw8nIaIP1FKvWAECkZUgmlBtq4DUZT3GNaTjgjyy9h2rTBRWSYOQa4uFpP44g9T38DuYPw8FMPH0dMl7CVICoyFabQNjWL5Zq5gR70X09XyutyNHyxy2tc |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwED6hghAMvBGFAhlYUyWxXScLUgVEIKqqQxHdLMcPqUtbtYXfjy9OoBVCDLDHD519r_ju-wButCaRxVIdbeIspNTqMNOEhcwy53wyFhWmBHHt8X4_HY2yQVVNuKjKKjGHth4oorTVqNwzbeuKOOzgxiwE20wS2k4IIxw7qTdd6NzBSz7MX78eEljqSfNcloRj6iaen6ZZc09r4KXfjHXpgfL9f9j7AexV4WfQ9fflEDbM5Ah2V0AJj-G2q-UMjWAw1lUpUXl6wdQGuKCcB27DY4xVQ43cAB7XI_CY0IsTeMkfhnePYcWyEKok7SzDRBXcxUhKYnpqC821wmcXo1LkE6WcWK4Ql1BKYpzCF1RRI3liDJUdlbpvT6ExmU7MGQQ8UsSmhZQZtVRHJI20IoWOM8kkcfrdhHYtXDHzYBoi_sQo9YIRKBhRCaYJ2eoRiGX5F8N6yhFBfhnbqs9LVHqJQ5Cpi8UkPv_D1NewPbjPRe-p_3wBOwkyAmNVGm1BYzl_M5ewpd6X48X8qryLH7Fc2Yk |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Adaptive+identification+of+linear+infinite-dimensional+systems&rft.jtitle=International+journal+of+control&rft.au=Chattopadhyay%2C+Sudipta&rft.au=Sukumar%2C+Srikant&rft.au=Natarajan%2C+Vivek&rft.date=2025-03-04&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=0020-7179&rft.eissn=1366-5820&rft.volume=98&rft.issue=3&rft.spage=593&rft.epage=608&rft_id=info:doi/10.1080%2F00207179.2024.2353731&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-7179&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-7179&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-7179&client=summon |