A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization
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arXiv
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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929533441015808 |
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| author | Teng, Sangli Iwasaki, Kaito Clark, William Yu, Xihang Bloch, Anthony Vasudevan, Ram Ghaffari, Maani |
| author_facet | Teng, Sangli Iwasaki, Kaito Clark, William Yu, Xihang Bloch, Anthony Vasudevan, Ram Ghaffari, Maani |
| contents | This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via a suitable selection of an entropy function and a bilinear symmetric metric. By relaxing the Casimir invariance requirement of the entropy function, this paper shows that the generalized formalism induces the free energy analogous to thermodynamics. The monotonic change of free energy can serve as a more precise criterion than mechanical energy or entropy alone. This paper provides examples of the generalized metriplectic system in a 2-dimensional Hamiltonian system and $\mathrm{SO}(3)$. This paper also provides a bilevel convex optimization approach for the identification of the metriplectic system given measurements of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization Teng, Sangli Iwasaki, Kaito Clark, William Yu, Xihang Bloch, Anthony Vasudevan, Ram Ghaffari, Maani Systems and Control This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via a suitable selection of an entropy function and a bilinear symmetric metric. By relaxing the Casimir invariance requirement of the entropy function, this paper shows that the generalized formalism induces the free energy analogous to thermodynamics. The monotonic change of free energy can serve as a more precise criterion than mechanical energy or entropy alone. This paper provides examples of the generalized metriplectic system in a 2-dimensional Hamiltonian system and $\mathrm{SO}(3)$. This paper also provides a bilevel convex optimization approach for the identification of the metriplectic system given measurements of the system. |
| title | A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.06233 |