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Gaussian Process-Based Nonlinear Moving Horizon Estimation

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Original languageEnglish
Number of pages16
JournalIEEE Transactions on Automatic Control
Publication statusAccepted/In press - 2025

Abstract

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we derive a sufficient condition under which incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in two simulation case studies and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions.

Keywords

    Gaussian Process, Machine learning, Moving Horizon Estimation, Nonlinear detectability, Nonlinear systems, State estimation

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Gaussian Process-Based Nonlinear Moving Horizon Estimation. / Wolff, Tobias M.; Lopez, Victor G.; Müller, Matthias A.
In: IEEE Transactions on Automatic Control, 2025.

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AU - Wolff, Tobias M.

AU - Lopez, Victor G.

AU - Müller, Matthias A.

N1 - © 2025 IEEE.

PY - 2025

Y1 - 2025

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KW - Machine learning

KW - Moving Horizon Estimation

KW - Nonlinear detectability

KW - Nonlinear systems

KW - State estimation

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