Nonlinear functional estimation: Functional detectability and full information estimation

• Published in: Automatica (Oxford) Vol. 171; p. 111945
• Main Authors: Muntwiler, Simon, Köhler, Johannes, Zeilinger, Melanie N.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2025
• Subjects: Full information estimation; Functional estimation; Incremental system properties; Nonlinear observer and filter design; Robust estimation; Functional estimation; Nonlinear observer and filter design; Full information estimation; Robust estimation; Incremental system properties
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2024.111945

We consider the design of functional estimators, i.e., approaches to compute an estimate of a nonlinear function of the state of a general nonlinear dynamical system subject to process noise based on noisy output measurements. To this end, we introduce a novel functional detectability notion in the form of incremental input/output-to-output stability (δ-IOOS). We show that δ-IOOS is a necessary condition for the existence of a functional estimator satisfying an input-to-output type stability property. Additionally, we prove that a system is functional detectable if and only if it admits a corresponding δ-IOOS Lyapunov function. Furthermore, δ-IOOS is shown to be a sufficient condition for the design of a stable functional estimator by introducing the design of a full information estimation (FIE) approach for functional estimation. Together, we present a unified framework to study functional estimation with a detectability condition, which is necessary and sufficient for the existence of a stable functional estimator, and a corresponding functional estimator design. The practical need for and applicability of the proposed functional estimator design is illustrated with a numerical example of a power system.