A switched-system ODE solver: Euler approximations, sampled-data observers and data assimilation.
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| Title: | A switched-system ODE solver: Euler approximations, sampled-data observers and data assimilation. |
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| Authors: | Al Hayzea, Aisha1 (AUTHOR), Das, Saptarshi1,2 (AUTHOR), Townley, Stuart1,3 (AUTHOR) s.b.townley@exeter.ac.uk |
| Source: | International Journal of Control. May2026, Vol. 99 Issue 5, p1601-1615. 15p. |
| Subjects: | Euler method, Data assimilation, Hybrid systems, Observability (Control theory), Numerical integration |
| Abstract: | This paper demonstrates how using state estimators in numerical integration schemes can significantly improve their performance. Here, we focus on the most straightforward situation of state prediction using a first-order forwards Euler scheme, which we combine with a classical Luenberger observer as the state estimator. By improved performance, we specifically mean that our new method can cope with time steps orders of magnitude greater than what is required for stability of the Euler method. We selected this simple case as the improved performance is easily quantified. The approach can be extended to other numerical prediction scheme/state estimator combinations. The numerical prediction method and the estimator are combined through a switching mechanism, leading to a hybrid system describing the overall numerical method. Stability and error analysis for the scheme is handled using input-state stability methods. By way of a corollary or alternative perspective, we show that the same hybrid switching method can be used for numerical, Euler-based predictions in the place of observer-based estimates to reduce the amount of output sampling required by the observer. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Control is the property of Taylor & Francis Ltd 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193710086 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A switched-system ODE solver: Euler approximations, sampled-data observers and data assimilation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Al+Hayzea%2C+Aisha%22">Al Hayzea, Aisha</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Das%2C+Saptarshi%22">Das, Saptarshi</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Townley%2C+Stuart%22">Townley, Stuart</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> s.b.townley@exeter.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Control%22">International Journal of Control</searchLink>. May2026, Vol. 99 Issue 5, p1601-1615. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Euler+method%22">Euler method</searchLink><br /><searchLink fieldCode="DE" term="%22Data+assimilation%22">Data assimilation</searchLink><br /><searchLink fieldCode="DE" term="%22Hybrid+systems%22">Hybrid systems</searchLink><br /><searchLink fieldCode="DE" term="%22Observability+%28Control+theory%29%22">Observability (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+integration%22">Numerical integration</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper demonstrates how using state estimators in numerical integration schemes can significantly improve their performance. Here, we focus on the most straightforward situation of state prediction using a first-order forwards Euler scheme, which we combine with a classical Luenberger observer as the state estimator. By improved performance, we specifically mean that our new method can cope with time steps orders of magnitude greater than what is required for stability of the Euler method. We selected this simple case as the improved performance is easily quantified. The approach can be extended to other numerical prediction scheme/state estimator combinations. The numerical prediction method and the estimator are combined through a switching mechanism, leading to a hybrid system describing the overall numerical method. Stability and error analysis for the scheme is handled using input-state stability methods. By way of a corollary or alternative perspective, we show that the same hybrid switching method can be used for numerical, Euler-based predictions in the place of observer-based estimates to reduce the amount of output sampling required by the observer. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Control is the property of Taylor & Francis Ltd 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193710086 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00207179.2025.2596134 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1601 Subjects: – SubjectFull: Euler method Type: general – SubjectFull: Data assimilation Type: general – SubjectFull: Hybrid systems Type: general – SubjectFull: Observability (Control theory) Type: general – SubjectFull: Numerical integration Type: general Titles: – TitleFull: A switched-system ODE solver: Euler approximations, sampled-data observers and data assimilation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Al Hayzea, Aisha – PersonEntity: Name: NameFull: Das, Saptarshi – PersonEntity: Name: NameFull: Townley, Stuart IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00207179 Numbering: – Type: volume Value: 99 – Type: issue Value: 5 Titles: – TitleFull: International Journal of Control Type: main |
| ResultId | 1 |
