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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 00207179 |
| DOI: | 10.1080/00207179.2025.2596134 |
