A Gradient-Based Optimization Algorithm for Optimal Control Problems With General Conformable Fractional Derivatives

This paper presents an extended gradient-based optimization framework for optimal control problems governed by general conformable fractional derivatives (GCFDs), which unify various fractional operators and provide greater modeling flexibility than classical conformable derivatives. The proposed st...

Full description

Saved in:

Bibliographic Details
Published in:	IEEE access Vol. 13; pp. 140270 - 140281
Main Authors:	Alaia, Essia Ben, Dhahri, Slim, Naifar, Omar
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Flexibility Fractional calculus general conformable derivative gradient-based optimization Heuristic algorithms Indexes Kernel Mathematical models numerical methods Numerical models Operators (mathematics) Optimal control Optimization Parameter sensitivity Sensitivity analysis System dynamics Terminal constraints Vectors
ISSN:	2169-3536, 2169-3536
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	This paper presents an extended gradient-based optimization framework for optimal control problems governed by general conformable fractional derivatives (GCFDs), which unify various fractional operators and provide greater modeling flexibility than classical conformable derivatives. The proposed study derives necessary optimality conditions for GCFD systems by reformulating the Hamiltonian and adjoint equations to accommodate the general operator. A novel discretization scheme with adaptive collocation points is introduced to efficiently handle kernel-dependent dynamics. Numerical experiments demonstrate the method's effectiveness, showing up to 20.2% improvement in terminal constraint satisfaction and 11.8% reduction in total cost compared to conformable-only approaches, with similar computational times. Comprehensive comparisons including Caputo derivatives demonstrate 17.8% cost reduction and 40.1% lower terminal state error. Parameter sensitivity analyses further validate kernel selection strategies. Overall, the proposed framework broadens the applicability of gradient-based optimization to a wider class of fractional-order systems, enhancing both performance and flexibility, with future work aimed at convergence analysis and real-world implementation.
AbstractList	This paper presents an extended gradient-based optimization framework for optimal control problems governed by general conformable fractional derivatives (GCFDs), which unify various fractional operators and provide greater modeling flexibility than classical conformable derivatives. The proposed study derives necessary optimality conditions for GCFD systems by reformulating the Hamiltonian and adjoint equations to accommodate the general operator. A novel discretization scheme with adaptive collocation points is introduced to efficiently handle kernel-dependent dynamics. Numerical experiments demonstrate the method’s effectiveness, showing up to 20.2% improvement in terminal constraint satisfaction and 11.8% reduction in total cost compared to conformable-only approaches, with similar computational times. Comprehensive comparisons including Caputo derivatives demonstrate 17.8% cost reduction and 40.1% lower terminal state error. Parameter sensitivity analyses further validate kernel selection strategies. Overall, the proposed framework broadens the applicability of gradient-based optimization to a wider class of fractional-order systems, enhancing both performance and flexibility, with future work aimed at convergence analysis and real-world implementation.
Author	Alaia, Essia Ben Naifar, Omar Dhahri, Slim
Author_xml	– sequence: 1 givenname: Essia Ben surname: Alaia fullname: Alaia, Essia Ben organization: Department of Computer Science, College of Computer and Information Sciences, Jouf University, Sakaka, Al-Jouf, Saudi Arabia – sequence: 2 givenname: Slim orcidid: 0000-0002-8677-460X surname: Dhahri fullname: Dhahri, Slim email: sdhahri@ju.edu.sa organization: Department of Computer Engineering and Networks, College of Computer and Information Sciences, Jouf University, Sakaka, Al-Jouf, Saudi Arabia – sequence: 3 givenname: Omar orcidid: 0000-0002-7929-5811 surname: Naifar fullname: Naifar, Omar organization: Control and Energy Management Laboratory, National School of Engineering, Sfax University, Sfax, Tunisia
BookMark	eNpNUVtLHDEUDkWhVv0F7UOgz7PmOkket1PdCoKClj6GTObEZpmdbJNRsL--2Y7YnjzkcL5LLt8HdDSlCRD6SMmKUmIu1l13eX-_YoTJFZemLv0OnTDamoZL3h79179H56VsSS1dR1KdoHmNN9kNEaa5-eIKDPh2P8dd_O3mmCa8Hh9TjvPPHQ4pL5AbcZemOacR3-XUj7Ar-Eel4A1MkBe0kneuQvgqO38wquOvkONzdX2GcoaOgxsLnL_up-j71eVD9625ud1cd-ubxvOWzg2TXklCnVPeOK2YHDzpW8WAeR045SpQ0QvTO9ULyY33oddaGtdT6UgA4KfoevEdktvafa6Xzy82uWj_DlJ-tC7P0Y9gaRgGKTnXSglRf1J7YhRrHR0UbYPg1evz4rXP6dcTlNlu01OuDyuWM6GoEEKTyuILy-dUSobwdiol9pCWXdKyh7Tsa1pV9WlRRQD4p6jFmdH8DxCikss
CODEN	IAECCG
Cites_doi	10.1155/int/5054424 10.1115/1.4000563 10.3934/math.2024522 10.1016/j.cam.2025.116526 10.3934/math.2023797 10.1007/978-3-030-11662-0 10.1137/18M1229845 10.1038/s41598-025-88277-w 10.1016/j.cam.2024.116169 10.1002/oca.2715 10.1109/ICSC58660.2023.10449793 10.1109/ICSC58660.2023.10449742 10.3390/math9131464 10.1016/j.cnsns.2018.04.019 10.1007/s10092-017-0213-8 10.1155/2022/4920540 10.1007/s10462-024-11023-7 10.3389/fenrg.2022.851070 10.1515/math-2023-0105 10.1016/j.amc.2006.08.105 10.1002/asjc.2797 10.1155/2020/3965269 10.1023/A:1021973025166 10.1016/j.ijnonlinmec.2018.10.001 10.1016/j.cam.2014.10.016 10.1016/j.chaos.2025.116007 10.1109/JSEN.2024.3524327 10.1080/00207179.2017.1350754 10.1155/2021/2817092
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025
DBID	97E ESBDL RIA RIE AAYXX CITATION 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D DOA
DOI	10.1109/ACCESS.2025.3595958
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005-present IEEE Open Access Journals IEEE All-Society Periodicals Package (ASPP) 1998-Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Engineered Materials Abstracts METADEX Technology Research Database Materials Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Materials Research Database Engineered Materials Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace METADEX Computer and Information Systems Abstracts Professional
DatabaseTitleList	Materials Research Database
Database_xml	– sequence: 1 dbid: DOA name: Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	2169-3536
EndPage	140281
ExternalDocumentID	oai_doaj_org_article_1fdd5533877440258c09726a1d716f43 10_1109_ACCESS_2025_3595958 11113298
Genre	orig-research
GrantInformation_xml	– fundername: Deanship of Graduate Studies and Scientific Research at Jouf University grantid: DGSSR-2023-02-02461
GroupedDBID	0R~ 4.4 5VS 6IK 97E AAJGR ABAZT ABVLG ACGFS ADBBV AGSQL ALMA_UNASSIGNED_HOLDINGS BCNDV BEFXN BFFAM BGNUA BKEBE BPEOZ EBS EJD ESBDL GROUPED_DOAJ IPLJI JAVBF KQ8 M43 M~E O9- OCL OK1 RIA RIE RNS AAYXX CITATION 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c361t-25c7501aa7c9a8725dc0b672e2c8f3137f14b49ba7b4539ccfb8859ab15a0fee3
IEDL.DBID	RIE
ISICitedReferencesCount	2
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001550810200021&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2169-3536
IngestDate	Fri Oct 03 12:25:50 EDT 2025 Sat Nov 01 15:14:21 EDT 2025 Sat Nov 29 07:36:20 EST 2025 Wed Aug 20 06:20:52 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Language	English
License	https://creativecommons.org/licenses/by-nc-nd/4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c361t-25c7501aa7c9a8725dc0b672e2c8f3137f14b49ba7b4539ccfb8859ab15a0fee3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-8677-460X 0000-0002-7929-5811
OpenAccessLink	https://ieeexplore.ieee.org/document/11113298
PQID	3247144480
PQPubID	4845423
PageCount	12
ParticipantIDs	crossref_primary_10_1109_ACCESS_2025_3595958 proquest_journals_3247144480 ieee_primary_11113298 doaj_primary_oai_doaj_org_article_1fdd5533877440258c09726a1d716f43
PublicationCentury	2000
PublicationDate	20250000 2025-00-00 20250101 2025-01-01
PublicationDateYYYYMMDD	2025-01-01
PublicationDate_xml	– year: 2025 text: 20250000
PublicationDecade	2020
PublicationPlace	Piscataway
PublicationPlace_xml	– name: Piscataway
PublicationTitle	IEEE access
PublicationTitleAbbrev	Access
PublicationYear	2025
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref13 ref12 ref15 ref14 Smith (ref17) 2024; 10 ref31 ref30 ref11 ref10 ref2 ref1 ref16 ref19 Wang (ref18) 2025; 101 ref24 ref23 ref26 ref25 ref20 ref22 ref21 ref28 ref27 ref29 ref8 ref7 ref9 ref4 ref3 ref6 ref5
References_xml	– ident: ref16 doi: 10.1155/int/5054424 – ident: ref31 doi: 10.1115/1.4000563 – ident: ref7 doi: 10.3934/math.2024522 – ident: ref22 doi: 10.1016/j.cam.2025.116526 – ident: ref12 doi: 10.3934/math.2023797 – ident: ref25 doi: 10.1007/978-3-030-11662-0 – ident: ref29 doi: 10.1137/18M1229845 – ident: ref19 doi: 10.1038/s41598-025-88277-w – ident: ref1 doi: 10.1016/j.cam.2024.116169 – volume: 10 start-page: 123 year: 2024 ident: ref17 article-title: Gradient descent methods in fractional calculus publication-title: Fractional Dyn. J. – ident: ref30 doi: 10.1002/oca.2715 – ident: ref6 doi: 10.1109/ICSC58660.2023.10449793 – volume: 101 year: 2025 ident: ref18 article-title: Adaptive control via conformable derivatives publication-title: Automatica – ident: ref5 doi: 10.1109/ICSC58660.2023.10449742 – ident: ref23 doi: 10.3390/math9131464 – ident: ref24 doi: 10.1016/j.cnsns.2018.04.019 – ident: ref4 doi: 10.1007/s10092-017-0213-8 – ident: ref13 doi: 10.1155/2022/4920540 – ident: ref15 doi: 10.1007/s10462-024-11023-7 – ident: ref11 doi: 10.3389/fenrg.2022.851070 – ident: ref27 doi: 10.1515/math-2023-0105 – ident: ref28 doi: 10.1016/j.amc.2006.08.105 – ident: ref14 doi: 10.1002/asjc.2797 – ident: ref9 doi: 10.1155/2020/3965269 – ident: ref26 doi: 10.1023/A:1021973025166 – ident: ref2 doi: 10.1016/j.ijnonlinmec.2018.10.001 – ident: ref3 doi: 10.1016/j.cam.2014.10.016 – ident: ref20 doi: 10.1016/j.chaos.2025.116007 – ident: ref21 doi: 10.1109/JSEN.2024.3524327 – ident: ref8 doi: 10.1080/00207179.2017.1350754 – ident: ref10 doi: 10.1155/2021/2817092
SSID	ssj0000816957
Score	2.347555
Snippet	This paper presents an extended gradient-based optimization framework for optimal control problems governed by general conformable fractional derivatives...
SourceID	doaj proquest crossref ieee
SourceType	Open Website Aggregation Database Index Database Publisher
StartPage	140270
SubjectTerms	Flexibility Fractional calculus general conformable derivative gradient-based optimization Heuristic algorithms Indexes Kernel Mathematical models numerical methods Numerical models Operators (mathematics) Optimal control Optimization Parameter sensitivity Sensitivity analysis System dynamics Terminal constraints Vectors
SummonAdditionalLinks	– databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07bxQxELZQlAIKREIQBwG5oGTJ2muvPeXlkkuKKKQAkc7yE5DIJbpb8vsZPwInUdCwpW3Z65m155vVzDeEvPNB6tEH1yWEI50QEDoX_NixJCy3aDSCK-z6F-ryUl9fw9VWqa8cE1bpgavgjlgKQSIm0SpT2XGpfSacGS0LiPSTKDyfvYItZ6rcwZqNIFWjGWI9HM0XC9wROoRcfsjJqJCLvG-ZosLY30qs_HUvF2OzfEaeNpRI5_Xt9sijuNonT7a4A5-TaU7P1iVea-qO0RQF-hFP_01Lq6TzH19v0e__dkMRldYunHBRA9PpVS0js6FfcAht1NO5t0BY7KLLdc14wOYTXPG-8INvDsjn5emnxXnXSih0fhjZ1HHpERIwa5UHqxWXwfduVDxyr9PABpWYcAKcVU7IAbxPTmsJ1jFp-xTj8ILsrG5X8SWhAngfRYjgWECz7twgvOMRQPkEqKMZef8gTXNXmTJM8TB6MFX4JgvfNOHPyHGW-O-hmea6NKDyTVO--ZfyZ-Qg6-vPevgMHHDywwcFmnYmNwaho0L3Uej-1f9Y-zV5nPdTf8cckp1p_TO-Ibv-fvq-Wb8tn-MvA8Dhhg priority: 102 providerName: Directory of Open Access Journals
Title	A Gradient-Based Optimization Algorithm for Optimal Control Problems With General Conformable Fractional Derivatives
URI	https://ieeexplore.ieee.org/document/11113298 https://www.proquest.com/docview/3247144480 https://doaj.org/article/1fdd5533877440258c09726a1d716f43
Volume	13
WOSCitedRecordID	wos001550810200021&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: PRVAON databaseName: Directory of Open Access Journals customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NTxQxFG-AeNADImJcBNKDRwamnXbaHpeV1YMgB4zcmn4qieya2YGjf7uvH3wkxoOXyaTttJ3-pn3vdfp-D6H3znPZO2-bCOpIw5jyjfWub0hkhhoQGt5mdv3P4vxcXl2pi-qsnn1hQgj58Fk4Srf5X75futu0VXZMSlx0uY7WheiLs9bDhkqKIKG4qMxCpFXH09kMXgJsQMqPkv-pSnHdn0ifTNJfo6r8tRRn-TJ_-Z8920KbVZHE04L8K7QWFtvoxRN6wddonOKPQz7SNTYnIK08_gILxE31vMTTn9-Xw_X44waD4lqyoMJZObuOL0qkmRX-BkVwZadOuVnLhSw8H4pTBCR_gBbvMoX4agd9nZ9ezj41NcpC47qejA3lDrQGYoxwykhBuXet7QUN1MnYkU5EwixT1gjLeKeci1ZKrowl3LQxhO4N2lgsF-EtwkzRNjAflCUeJL-1HXOWBqWEi8p7PkGH96OvfxUyDZ2NkFbpApZOYOkK1gSdJIQeiiYm7JwAQ6_rxNIkQsWgs0qRqA4ply4REvWGeLAEI-smaCfB9dheRWqC9u4B13XarjRolwIsTCbb3X889g49T10smzB7aGMcbsM-eubuxuvVcJAterie_T49yF_nH-nR4v0
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NbxQhFCdaTbQHP2u6WpWDR6cdGBjguF1da1zXHmrsjfCpTeyumZ327_fx0drEePA2AQYYfgPvPeD9HkJvnOeyd942EdSRhjHlG-td35DIDDUgNLzN7PoLsVzK01N1XJ3Vsy9MCCFfPgv76TGf5fu1u0hbZQekxEWXt9Edzhhti7vW9ZZKiiGhuKjcQqRVB9PZDD4DrEDK95MHqkqR3W_In0zTX-Oq_LUYZwkzf_iffXuEHlRVEk8L9o_RrbB6grZvEAw-ReMUfxjypa6xOQR55fEXWCLOq-8lnv78vh7Oxh_nGFTXkgUVzsrtdXxcYs1s8Dcogis_dcrNei5k4flQ3CIg-R20eJlJxDc76Ov8_cnsqKlxFhrX9WRsKHegNxBjhFNGCsq9a20vaKBOxo50IhJmmbJGWMY75Vy0UnJlLOGmjSF0z9DWar0KuwgzRdvAfFCWeJD91nbMWRqUEi4q7_kEvb0aff2r0GnobIa0ShewdAJLV7Am6DAhdF00cWHnBBh6XaeWJhEqBq1VikR2SLl0iZKoN8SDLRhZN0E7Ca4_7VWkJmjvCnBdJ-5Gg34pwMZksn3-j9deo3tHJ58XevFx-ekFup-6W7Zk9tDWOFyEl-iuuxzPNsOr_Hf-BijK5B4
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=A+Gradient-Based+Optimization+Algorithm+for+Optimal+Control+Problems+With+General+Conformable+Fractional+Derivatives&rft.jtitle=IEEE+access&rft.au=Alaia%2C+Essia+Ben&rft.au=Dhahri%2C+Slim&rft.au=Naifar%2C+Omar&rft.date=2025&rft.pub=IEEE&rft.eissn=2169-3536&rft.volume=13&rft.spage=140270&rft.epage=140281&rft_id=info:doi/10.1109%2FACCESS.2025.3595958&rft.externalDocID=11113298
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2169-3536&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2169-3536&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2169-3536&client=summon