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arXiv · 2403.15055

Optimal control of gradient flows via the Weighted Energy-Dissipation method

Takeshi Fukao·Ulisse Stefanelli·Riccardo Voso
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Abstract

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 $\Gamma$-convergence analysis we show that penalised optimal controls converge to nonpenalized one as the approximation is removed.

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Takeshi Fukao, Ulisse Stefanelli, Riccardo Voso. 2024-03-22. Optimal control of gradient flows via the Weighted Energy-Dissipation method. https://arxiv.org/abs/2403.15055

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