Boundary Control for Wildfire Mitigation
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912580225728512 |
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| author | Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Georges, Didier |
| author_facet | Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Georges, Didier |
| contents | In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study two cases. First, when the wind velocity is known, we design a Neumann-type boundary controller guaranteeing that the temperature of some protected region converges exponentially, in the $L^2$ norm, to the ambient temperature. Second, when the wind velocity is unknown, we design an adaptive Neumann-type boundary controller guaranteeing the asymptotic convergence, in the $L^2$ norm, of the temperature of the protected region to the ambient temperature. In both cases, the controller acts along the boundary of the protected region and relies solely on temperature measurements along that boundary. Our results are supported by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Control for Wildfire Mitigation Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Georges, Didier Analysis of PDEs In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study two cases. First, when the wind velocity is known, we design a Neumann-type boundary controller guaranteeing that the temperature of some protected region converges exponentially, in the $L^2$ norm, to the ambient temperature. Second, when the wind velocity is unknown, we design an adaptive Neumann-type boundary controller guaranteeing the asymptotic convergence, in the $L^2$ norm, of the temperature of the protected region to the ambient temperature. In both cases, the controller acts along the boundary of the protected region and relies solely on temperature measurements along that boundary. Our results are supported by numerical simulations. |
| title | Boundary Control for Wildfire Mitigation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.08631 |