Gaussian Process-Based Nonlinear Moving Horizon Estimation

• 成果类型: Article
• 署名作者: Wolff, Tobias M.; Lopez, Victor G.; Mueller, Matthias A.
• 署名单位: Leibniz University Hannover
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3580033
• 发表日期: 2025
• 关键词: State estimation; observers; algorithm

摘要

In this article, we propose a novel Gaussian process (GP)-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 GPs. On the other hand, we exploit the posterior variances of the GPs 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 an 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.