Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees Article Swipe
Negin Musavi
,
Ziyao Guo
,
Geir E. Dullerud
,
Yingying Li
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.00656
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.00656
This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system identification methods: least-squares estimation (LSE), which is a point estimation method; and set-membership estimation (SME), which estimates an uncertainty set that contains the true parameters. We provide non-asymptotic convergence rates for LSE and SME under i.i.d. control inputs and control policies with i.i.d. random perturbations, both of which are considered as non-active-exploration inputs. Compared with the counter-example based on piecewise-affine systems in the literature, the success of non-active exploration in our setting relies on a key assumption on the system dynamics: we require the system functions to be real-analytic. Our results, together with the piecewise-affine counter-example, reveal the importance of differentiability in nonlinear system identification through non-active exploration. Lastly, we numerically compare our theoretical bounds with the empirical performance of LSE and SME on a pendulum example and a quadrotor example.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2411.00656
- https://arxiv.org/pdf/2411.00656
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W4404345588Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2411.00656Digital Object Identifier
- Title
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Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic GuaranteesWork title
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preprintOpenAlex work type
- Language
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enPrimary language
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2024Year of publication
- Publication date
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2024-11-01Full publication date if available
- Authors
-
Negin Musavi, Ziyao Guo, Geir E. Dullerud, Yingying LiList of authors in order
- Landing page
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https://arxiv.org/abs/2411.00656Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2411.00656Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2411.00656Direct OA link when available
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Identification (biology), Nonlinear system, Applied mathematics, Nonlinear dynamical systems, Dynamical systems theory, Mathematics, Computer science, Control theory (sociology), Physics, Artificial intelligence, Biology, Control (management), Botany, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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