Details
| Original language | English |
|---|---|
| Pages (from-to) | 7466-7481 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 68 |
| Issue number | 12 |
| Early online date | 5 Dec 2023 |
| Publication status | Published - Dec 2023 |
Abstract
Keywords
- eess.SY, cs.SY, Robust stability, Stability criteria, Estimation, Observers, state estimation, Incremental system properties, moving horizon estimation, Noise measurement, Standards, Lyapunov methods, moving horizon estimation (MHE)
ASJC Scopus subject areas
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Computer Science Applications
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In: IEEE Transactions on Automatic Control, Vol. 68, No. 12, 12.2023, p. 7466-7481.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Lyapunov function for robust stability of moving horizon estimation
AU - Schiller, Julian D.
AU - Muntwiler, Simon
AU - Köhler, Johannes
AU - Zeilinger, Melanie N.
AU - Müller, Matthias A.
PY - 2023/12
Y1 - 2023/12
N2 - We provide a novel robust stability analysis for moving horizon estimation (MHE) using a Lyapunov function. Additionally, we introduce linear matrix inequalities (LMIs) to verify the necessary incremental input/output-to-state stability (δ-IOSS) detectability condition. We consider an MHE formulation with time-discounted quadratic objective for nonlinear systems admitting an exponential δ-IOSS Lyapunov function. We show that with a suitable parameterization of the MHE objective, the δ-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 δ-IOSS can be relaxed. Moreover, we provide simple LMI conditions to systematically derive δ-IOSS Lyapunov functions, which allows us to easily verify δ-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 δ-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.
AB - We provide a novel robust stability analysis for moving horizon estimation (MHE) using a Lyapunov function. Additionally, we introduce linear matrix inequalities (LMIs) to verify the necessary incremental input/output-to-state stability (δ-IOSS) detectability condition. We consider an MHE formulation with time-discounted quadratic objective for nonlinear systems admitting an exponential δ-IOSS Lyapunov function. We show that with a suitable parameterization of the MHE objective, the δ-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 δ-IOSS can be relaxed. Moreover, we provide simple LMI conditions to systematically derive δ-IOSS Lyapunov functions, which allows us to easily verify δ-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 δ-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.
KW - eess.SY
KW - cs.SY
KW - Robust stability
KW - Stability criteria
KW - Estimation
KW - Observers
KW - state estimation
KW - Incremental system properties
KW - moving horizon estimation
KW - Noise measurement
KW - Standards
KW - Lyapunov methods
KW - moving horizon estimation (MHE)
UR - http://www.scopus.com/inward/record.url?scp=85161059119&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2202.12744
DO - 10.48550/arXiv.2202.12744
M3 - Article
VL - 68
SP - 7466
EP - 7481
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 12
ER -