Robust Model Reference Adaptive Control Based on Reproducing Kernel Hilbert Spaces.
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| Title: | Robust Model Reference Adaptive Control Based on Reproducing Kernel Hilbert Spaces. |
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| Authors: | Wang, Haoran1 (AUTHOR), Kurdila, Andrew J.1 (AUTHOR), L'Afflitto, Andrea2 (AUTHOR) a.lafflitto@vt.edu, Oesterheld, Derek3 (AUTHOR), Stilwell, Daniel J.3 (AUTHOR) |
| Source: | International Journal of Adaptive Control & Signal Processing. Jun2025, Vol. 39 Issue 6, p1128-1148. 21p. |
| Subjects: | Distributed parameter systems, Adaptive control systems, Ordinary differential equations, Hilbert space, Robust control |
| Abstract: | This article introduces native space embedding for robust adaptive control of ordinary differential equations that contain vector‐valued functional uncertainties in a reproducing kernel Hilbert space (RKHS). The proposed approach is based on a two‐phase method for analyzing and designing adaptive controllers. In the first phase, a limiting distributed parameter system (DPS), which describes the ideal closed‐loop system's performance, is introduced. The limiting DPS is not realizable in practice since it evolves in a generally infinite‐dimensional space. In the second phase, consistent finite‐dimensional approximations of the DPS are introduced to determine realizable controllers. Uniform ultimate bounds on the trajectory tracking error dynamics are derived for the functional uncertainty classes contained in the native space. These bounds are derived in terms of the power function of the RKHS or in terms of the fill distance of centers that define the scattered basis for approximations. Two numerical examples demonstrate the applicability of the proposed results. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Adaptive Control & Signal Processing is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 185726181 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Robust Model Reference Adaptive Control Based on Reproducing Kernel Hilbert Spaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wang%2C+Haoran%22">Wang, Haoran</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kurdila%2C+Andrew+J%2E%22">Kurdila, Andrew J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22L'Afflitto%2C+Andrea%22">L'Afflitto, Andrea</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> a.lafflitto@vt.edu</i><br /><searchLink fieldCode="AR" term="%22Oesterheld%2C+Derek%22">Oesterheld, Derek</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Stilwell%2C+Daniel+J%2E%22">Stilwell, Daniel J.</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Adaptive+Control+%26+Signal+Processing%22">International Journal of Adaptive Control & Signal Processing</searchLink>. Jun2025, Vol. 39 Issue 6, p1128-1148. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Distributed+parameter+systems%22">Distributed parameter systems</searchLink><br /><searchLink fieldCode="DE" term="%22Adaptive+control+systems%22">Adaptive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This article introduces native space embedding for robust adaptive control of ordinary differential equations that contain vector‐valued functional uncertainties in a reproducing kernel Hilbert space (RKHS). The proposed approach is based on a two‐phase method for analyzing and designing adaptive controllers. In the first phase, a limiting distributed parameter system (DPS), which describes the ideal closed‐loop system's performance, is introduced. The limiting DPS is not realizable in practice since it evolves in a generally infinite‐dimensional space. In the second phase, consistent finite‐dimensional approximations of the DPS are introduced to determine realizable controllers. Uniform ultimate bounds on the trajectory tracking error dynamics are derived for the functional uncertainty classes contained in the native space. These bounds are derived in terms of the power function of the RKHS or in terms of the fill distance of centers that define the scattered basis for approximations. Two numerical examples demonstrate the applicability of the proposed results. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Adaptive Control & Signal Processing is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/acs.3997 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 1128 Subjects: – SubjectFull: Distributed parameter systems Type: general – SubjectFull: Adaptive control systems Type: general – SubjectFull: Ordinary differential equations Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Robust control Type: general Titles: – TitleFull: Robust Model Reference Adaptive Control Based on Reproducing Kernel Hilbert Spaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wang, Haoran – PersonEntity: Name: NameFull: Kurdila, Andrew J. – PersonEntity: Name: NameFull: L'Afflitto, Andrea – PersonEntity: Name: NameFull: Oesterheld, Derek – PersonEntity: Name: NameFull: Stilwell, Daniel J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 08906327 Numbering: – Type: volume Value: 39 – Type: issue Value: 6 Titles: – TitleFull: International Journal of Adaptive Control & Signal Processing Type: main |
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