Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909082441482240 |
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| author | Herty, Michael Thein, Ferdinand |
| author_facet | Herty, Michael Thein, Ferdinand |
| contents | We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $L^2$ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12006 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws Herty, Michael Thein, Ferdinand Optimization and Control Analysis of PDEs 35L50, 35Q93, 93D05 We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $L^2$ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process. |
| title | Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws |
| topic | Optimization and Control Analysis of PDEs 35L50, 35Q93, 93D05 |
| url | https://arxiv.org/abs/2207.12006 |