Optimal control of gradient flows via the Weighted Energy-Dissipation method
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911809216184320 |
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| author | Fukao, Takeshi Stefanelli, Ulisse Voso, Riccardo |
| author_facet | Fukao, Takeshi Stefanelli, Ulisse Voso, Riccardo |
| contents | We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation variational approach. This consists in the minimization of global-in-time functionals over trajectories, combined with a limit passage. We show that the original nonpenalized problem and the two successive approximations admits solutions. Moreover, resorting to a $Γ$-convergence analysis we show that penalised optimal controls converge to nonpenalized one as the approximation is removed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control of gradient flows via the Weighted Energy-Dissipation method Fukao, Takeshi Stefanelli, Ulisse Voso, Riccardo Optimization and Control 35K55, 49J27 We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation variational approach. This consists in the minimization of global-in-time functionals over trajectories, combined with a limit passage. We show that the original nonpenalized problem and the two successive approximations admits solutions. Moreover, resorting to a $Γ$-convergence analysis we show that penalised optimal controls converge to nonpenalized one as the approximation is removed. |
| title | Optimal control of gradient flows via the Weighted Energy-Dissipation method |
| topic | Optimization and Control 35K55, 49J27 |
| url | https://arxiv.org/abs/2403.15055 |