Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original sys...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-12-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.34768/amcs-2020-0045 |
| _version_ | 1818586848240336896 |
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| author | Chaturantabut Saifon |
| author_facet | Chaturantabut Saifon |
| author_sort | Chaturantabut Saifon |
| collection | DOAJ |
| description | This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem. |
| first_indexed | 2024-12-16T08:59:29Z |
| format | Article |
| id | doaj.art-810f84ce5713488f9220e3a543d4dab6 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-16T08:59:29Z |
| publishDate | 2020-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-810f84ce5713488f9220e3a543d4dab62022-12-21T22:37:13ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922020-12-0130461562810.34768/amcs-2020-0045amcs-2020-0045Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving frameworkChaturantabut Saifon0Department of Mathematics and Statistics, Thammasat University, Pathum Thani 12120, ThailandThis work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.https://doi.org/10.34768/amcs-2020-0045model order reductioncontractivityordinary differential equationspartial differential equationsproper orthogonal decompositiondiscrete empirical interpolation method |
| spellingShingle | Chaturantabut Saifon Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework International Journal of Applied Mathematics and Computer Science model order reduction contractivity ordinary differential equations partial differential equations proper orthogonal decomposition discrete empirical interpolation method |
| title | Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework |
| title_full | Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework |
| title_fullStr | Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework |
| title_full_unstemmed | Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework |
| title_short | Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework |
| title_sort | stabilized model reduction for nonlinear dynamical systems through a contractivity preserving framework |
| topic | model order reduction contractivity ordinary differential equations partial differential equations proper orthogonal decomposition discrete empirical interpolation method |
| url | https://doi.org/10.34768/amcs-2020-0045 |
| work_keys_str_mv | AT chaturantabutsaifon stabilizedmodelreductionfornonlineardynamicalsystemsthroughacontractivitypreservingframework |