Identifiability and Observability of Nonsmooth Systems via Taylor-like Approximations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910374093127680 |
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| author | Stechlinski, Peter Eisa, Sameh Abdelfattah, Hesham |
| author_facet | Stechlinski, Peter Eisa, Sameh Abdelfattah, Hesham |
| contents | New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic calculus is used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are: (i) practically implementable and amenable to large-scale problems; (ii) accurate since they directly treat the nonsmoothness while avoiding, e.g., smoothing approximations; and (iii) analogous to (and indeed recover) their smooth counterparts. To accomplish this, a first-order Taylor-like approximation theory is developed using lexicographic differentiation to directly treat nonsmooth functions. A practically implementable algorithm is proposed that determines partial structural identifiability or observability, a useful characterization in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identifiability and Observability of Nonsmooth Systems via Taylor-like Approximations Stechlinski, Peter Eisa, Sameh Abdelfattah, Hesham Optimization and Control New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic calculus is used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are: (i) practically implementable and amenable to large-scale problems; (ii) accurate since they directly treat the nonsmoothness while avoiding, e.g., smoothing approximations; and (iii) analogous to (and indeed recover) their smooth counterparts. To accomplish this, a first-order Taylor-like approximation theory is developed using lexicographic differentiation to directly treat nonsmooth functions. A practically implementable algorithm is proposed that determines partial structural identifiability or observability, a useful characterization in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling. |
| title | Identifiability and Observability of Nonsmooth Systems via Taylor-like Approximations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.12930 |