at Google ScholarTitle data
Schiller, Julian D. ; Grüne, Lars ; Müller, Matthias A.:
Performance guarantees for optimization-based state estimation using turnpike properties.
Bayreuth ; Hannover
,
2025
. - 16 p.
DOI: https://doi.org/10.48550/arXiv.2501.18385
Project information
| Project title: |
Project's official title Project's id Stochastic Optimal Control and MPC – Dissipativity, Risk and Performance GR 1569/25-1, BA 7477/3-1, project no. 499435839 Robuste Stabilität und Suboptimalität bei der Zustandsschätzung mit bewegtem Horizont---Von konzeptionellen zu praktisch relevanten Garantien project no. 426459964 |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract in another language
In this paper, we develop novel accuracy and performance guarantees for optimal state estimation of general nonlinear systems (in particular, moving horizon estimation, MHE). Our results rely on a turnpike property of the optimal state estimation problem, which essentially states that the omniscient infinite-horizon solution involving all past and future data serves as turnpike for the solutions of finite-horizon estimation problems involving a subset of the data. This leads to the surprising observation that MHE problems naturally exhibit a leaving arc, which may have a strong negative impact on the estimation accuracy. To address this, we propose a delayed MHE scheme, and we show that the resulting performance (both averaged and non-averaged) is approximately optimal and achieves bounded dynamic regret with respect to the infinite-horizon solution, with error terms that can be made arbitrarily small by an appropriate choice of the delay. In various simulation examples, we observe that already a very small delay in the MHE scheme is sufficient to significantly improve the overall estimation error by 20-25 % compared to standard MHE (without delay). This finding is of great importance for practical applications (especially for monitoring, fault detection, and parameter estimation) where a small delay in the estimation is rather irrelevant but may significantly improve the estimation results.