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New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic derivatives are used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are practically implementable, accurate, and analogous to (and indeed recover) their smooth counterparts. To accomplish this, a novel first-order Taylor-like approximation theory is developed to directly treat nonsmooth (i.e., continuous but nondifferentiable) functions. An L-SERC algorithm is proposed that determines partial structural identifiability or observability, which are useful characterizations in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling.
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Parameter Identifiability and Reduction for Smooth and Nonsmooth Differential-Algebraic Equation Systems
We extend the sensitivity rank condition (SERC), which tests for identifiability of smooth input-output systems, to a broader class of systems. Particularly, we build on our recently developed lexicographic SERC (L-SERC) theory and methods to achieve an identifiability test for differential-algebraic equation (DAE) systems for the first time, including nonsmooth systems. Additionally, we develop a method to determine the identifiable and non-identifiable parameter sets. We show how this new theory can be used to establish a (non-local) parameter reduction procedure and we show how parameter estimation problems can be solved. We apply the new methods to problems in wind turbine power systems and glucose-insulin kinetics.
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- PAR ID:
- 10582562
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers Inc.
- Date Published:
- Journal Name:
- IEEE Control Systems Letters
- Volume:
- 8
- ISSN:
- 2475-1456
- Page Range / eLocation ID:
- 3159 to 3164
- Subject(s) / Keyword(s):
- Differential algebraic systems nonlinear systems identification hybrid systems.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1109/LCSYS.2024.3521427
