A Lyapunov Function for Robust Stability of Moving Horizon Estimation

• 成果类型: Article
• 署名作者: Schiller, Julian D.; Muntwiler, Simon; Koehler, Johannes; Zeilinger, Melanie N.; Mueller, Matthias A.
• 署名单位: Leibniz University Hannover; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3280344
• 发表日期: 2023
• 页码: 7466-7481
• 关键词: Incremental system properties; moving horizon estimation (MHE); State estimation

摘要

We provide a novel robust stability analysis for moving horizon estimation (MHE) using a Lyapunov function. In addition, we introduce linear matrix inequalities (LMIs) to verify the necessary incremental input/output-to-state stability (delta-IOSS) detectability condition. We consider an MHE formulation with time-discounted quadratic objective for nonlinear systems admitting an exponential delta-IOSS Lyapunov function. We show that with a suitable parameterization of the MHE objective, the delta-IOSS Lyapunov function serves as an M-step Lyapunov function for MHE. Provided that the estimation horizon is chosen large enough, this directly implies exponential stability of MHE. The stability analysis is also applicable to full information estimation, where the restriction to exponential delta-IOSS can be relaxed. Moreover, we provide simple LMI conditions to systematically derive delta-IOSS Lyapunov functions, which allows us to easily verify delta-IOSS for a large class of nonlinear detectable systems. This is useful in the context of MHE in general, since most of the existing nonlinear (robust) stability results for MHE depend on the system being delta-IOSS (detectable). In combination, we thus provide a framework for designing MHE schemes with guaranteed robust exponential stability. The applicability of the proposed methods is demonstrated with a nonlinear chemical reactor process and a 12-state quadrotor model.