Details
Original language | English |
---|---|
Number of pages | 16 |
Journal | IEEE Transactions on Automatic Control |
Publication status | Accepted/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
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Computer Science Applications
- Engineering(all)
- Electrical and Electronic Engineering
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In: IEEE Transactions on Automatic Control, 2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Gaussian Process-Based Nonlinear Moving Horizon Estimation
AU - Wolff, Tobias M.
AU - Lopez, Victor G.
AU - Müller, Matthias A.
N1 - © 2025 IEEE.
PY - 2025
Y1 - 2025
N2 - 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.
AB - 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.
KW - Gaussian Process
KW - Machine learning
KW - Moving Horizon Estimation
KW - Nonlinear detectability
KW - Nonlinear systems
KW - State estimation
UR - http://www.scopus.com/inward/record.url?scp=105008766671&partnerID=8YFLogxK
U2 - 10.1109/TAC.2025.3580033
DO - 10.1109/TAC.2025.3580033
M3 - Article
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
ER -