Spatial decay of perturbations in hyperbolic equations with optimal boundary control
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915155510558720 |
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| author | Oppeneiger, Benedikt Schaller, Manuel Worthmann, Karl |
| author_facet | Oppeneiger, Benedikt Schaller, Manuel Worthmann, Karl |
| contents | Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally controlled evolution equations. In the present paper we analyze a chain of transport equations with boundary and point controls with regard to this property. Both for Dirichlet and Neumann boundary and coupling conditions, we show a necessary and sufficient criterion on control domains which allow for the domain-uniform stabilization of this equation. We illustrate the results by means of a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatial decay of perturbations in hyperbolic equations with optimal boundary control Oppeneiger, Benedikt Schaller, Manuel Worthmann, Karl Optimization and Control Systems and Control Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally controlled evolution equations. In the present paper we analyze a chain of transport equations with boundary and point controls with regard to this property. Both for Dirichlet and Neumann boundary and coupling conditions, we show a necessary and sufficient criterion on control domains which allow for the domain-uniform stabilization of this equation. We illustrate the results by means of a numerical example. |
| title | Spatial decay of perturbations in hyperbolic equations with optimal boundary control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2502.11975 |