Geometric insight into linear augmented observers for uncertain systems.
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| Title: | Geometric insight into linear augmented observers for uncertain systems. |
|---|---|
| Authors: | Li, Junhui1 (AUTHOR) jh.li@gxu.edu.cn, Gong, Beili1 (AUTHOR) aublgong@gxu.edu.cn |
| Source: | ISA Transactions. May2026, Vol. 172, p211-220. 10p. |
| Subjects: | Observability (Control theory), Invariant subspaces, Noise measurement, Uncertain systems, Estimation bias |
| Abstract: | Linear augmented observers (LAOs) are widely used for state and uncertainty estimation in practical control systems, yet their structural limitations remain unclear. Existing analyses typically assume that the augmented system is observable a priori and do not examine how the nominal model structure limits estimation performance. This paper develops a geometric framework to characterize the structural limitations of LAOs for uncertain systems with linear nominal models. A necessary and sufficient condition for the observability of the augmented system is established in terms of the invariant zeros of the nominal model, which removes the need for prior observability assumptions. The estimation error is shown to be confined to a subspace structurally determined by the weakly unobservable subspace of the nominal model, which explicitly reveals how the nominal system structure limits attainable estimation accuracy. In particular, arbitrarily small estimation error is achievable if and only if the nominal model has no invariant zeros. The complete set of state–uncertainty combinations that are estimable via high-bandwidth LAOs is explicitly characterized. In addition, the exponential amplification of measurement noise as observer bandwidth increases is analytically quantified. These results provide explicit and verifiable structural criteria for assessing the feasibility and attainable accuracy of state and uncertainty estimation using LAOs. Numerical simulations validate the theoretical findings. • A necessary and sufficient structural condition for the observability of the augmented system is established, providing a rigorous geometric characterization of LAO feasibility in terms of invariant zeros of the nominal system, without relying on ad hoc observability assumptions. • The estimation error of high-bandwidth LAOs is shown to be confined to a subspace structurally determined by the weakly unobservable subspace of the nominal system, highlighting that the nominal system structure imposes intrinsic limitations on the estimation accuracy and providing guidance for observer bandwidth selection, independent of specific disturbance realizations. • The estimable combinations of system states and uncertainties for high-bandwidth LAOs are geometrically characterized and shown to correspond to those whose combination matrices project out the estimation-error component associated with the weakly unobservable subspace, thereby identifying the quantities accessible to LAO-based estimation and admissible for observer-based control. • A quantitative analysis of measurement noise sensitivity in LAO-based estimation is developed, showing how increasing observer bandwidth can exponentially amplify noise and revealing the fundamental trade-off between bandwidth and achievable estimation performance. [ABSTRACT FROM AUTHOR] |
| Copyright of ISA Transactions is the property of Elsevier B.V. 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: 192840316 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Geometric insight into linear augmented observers for uncertain systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Junhui%22">Li, Junhui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jh.li@gxu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Gong%2C+Beili%22">Gong, Beili</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aublgong@gxu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22ISA+Transactions%22">ISA Transactions</searchLink>. May2026, Vol. 172, p211-220. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Observability+%28Control+theory%29%22">Observability (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Invariant+subspaces%22">Invariant subspaces</searchLink><br /><searchLink fieldCode="DE" term="%22Noise+measurement%22">Noise measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertain+systems%22">Uncertain systems</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+bias%22">Estimation bias</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Linear augmented observers (LAOs) are widely used for state and uncertainty estimation in practical control systems, yet their structural limitations remain unclear. Existing analyses typically assume that the augmented system is observable a priori and do not examine how the nominal model structure limits estimation performance. This paper develops a geometric framework to characterize the structural limitations of LAOs for uncertain systems with linear nominal models. A necessary and sufficient condition for the observability of the augmented system is established in terms of the invariant zeros of the nominal model, which removes the need for prior observability assumptions. The estimation error is shown to be confined to a subspace structurally determined by the weakly unobservable subspace of the nominal model, which explicitly reveals how the nominal system structure limits attainable estimation accuracy. In particular, arbitrarily small estimation error is achievable if and only if the nominal model has no invariant zeros. The complete set of state–uncertainty combinations that are estimable via high-bandwidth LAOs is explicitly characterized. In addition, the exponential amplification of measurement noise as observer bandwidth increases is analytically quantified. These results provide explicit and verifiable structural criteria for assessing the feasibility and attainable accuracy of state and uncertainty estimation using LAOs. Numerical simulations validate the theoretical findings. • A necessary and sufficient structural condition for the observability of the augmented system is established, providing a rigorous geometric characterization of LAO feasibility in terms of invariant zeros of the nominal system, without relying on ad hoc observability assumptions. • The estimation error of high-bandwidth LAOs is shown to be confined to a subspace structurally determined by the weakly unobservable subspace of the nominal system, highlighting that the nominal system structure imposes intrinsic limitations on the estimation accuracy and providing guidance for observer bandwidth selection, independent of specific disturbance realizations. • The estimable combinations of system states and uncertainties for high-bandwidth LAOs are geometrically characterized and shown to correspond to those whose combination matrices project out the estimation-error component associated with the weakly unobservable subspace, thereby identifying the quantities accessible to LAO-based estimation and admissible for observer-based control. • A quantitative analysis of measurement noise sensitivity in LAO-based estimation is developed, showing how increasing observer bandwidth can exponentially amplify noise and revealing the fundamental trade-off between bandwidth and achievable estimation performance. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of ISA Transactions is the property of Elsevier B.V. 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: 10.1016/j.isatra.2026.03.015 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 211 Subjects: – SubjectFull: Observability (Control theory) Type: general – SubjectFull: Invariant subspaces Type: general – SubjectFull: Noise measurement Type: general – SubjectFull: Uncertain systems Type: general – SubjectFull: Estimation bias Type: general Titles: – TitleFull: Geometric insight into linear augmented observers for uncertain systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Junhui – PersonEntity: Name: NameFull: Gong, Beili IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00190578 Numbering: – Type: volume Value: 172 Titles: – TitleFull: ISA Transactions Type: main |
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