Weakly coupled systems of eikonal equations for autonomous vehicles
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909207430692864 |
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| author | Chiri, Maria Teresa Czuprynski, Kenneth D Zikatanov, Ludmil T |
| author_facet | Chiri, Maria Teresa Czuprynski, Kenneth D Zikatanov, Ludmil T |
| contents | In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes into account two types of breakdown for the vehicle, partial and total, which happen at a known, spatially inhomogeneous rate. In particular, we analyze the complications due to the delicate degenerate coupling condition by using existing results on weakly coupled systems of Hamilton-Jacobi equations. Then we consider finite element method schemes built for convection-diffusion problems to construct approximate solutions for this system and produce some numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02966 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weakly coupled systems of eikonal equations for autonomous vehicles Chiri, Maria Teresa Czuprynski, Kenneth D Zikatanov, Ludmil T Optimization and Control 65N30, 35Q93, 65K10 In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes into account two types of breakdown for the vehicle, partial and total, which happen at a known, spatially inhomogeneous rate. In particular, we analyze the complications due to the delicate degenerate coupling condition by using existing results on weakly coupled systems of Hamilton-Jacobi equations. Then we consider finite element method schemes built for convection-diffusion problems to construct approximate solutions for this system and produce some numerical simulations. |
| title | Weakly coupled systems of eikonal equations for autonomous vehicles |
| topic | Optimization and Control 65N30, 35Q93, 65K10 |
| url | https://arxiv.org/abs/2310.02966 |