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Optimal state estimation : Turnpike analysis and performance results

Title data

Schiller, Julian D. ; Grüne, Lars ; Müller, Matthias A.:
Optimal state estimation : Turnpike analysis and performance results.
Bayreuth ; Hannover , 2024 . - 8 p.
DOI: https://doi.org/10.48550/arXiv.2409.14873

Official URL: Volltext

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 introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the solutions of truncated problems involving only a subset of the data. We consider two different mathematical characterizations of this phenomenon and provide corresponding sufficient conditions that rely on strict dissipativity and decaying sensitivity. As second contribution, we show how a specific turnpike property can be used to establish performance guarantees when approximating the optimal solution of the full problem by a sequence of truncated problems, and we show that the resulting performance (both averaged and non-averaged) is approximately optimal with error terms that can be made arbitrarily small by an appropriate choice of the horizon length. In addition, we discuss interesting implications of these results for the practically relevant case of moving horizon estimation and illustrate our results with a numerical example.

Further data

Item Type: Preprint, postprint
Keywords: moving horizon estimation; turnpike property; performance estimates
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 Oct 2024 08:34
Last Modified: 04 Oct 2024 08:34
URI: https://eref.uni-bayreuth.de/id/eprint/90542