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Pré-Publication, Document De Travail Année : 2024

A non linear optimal control problem related to a road de-icing device: Analysis and Numerical experiments

Résumé

In order to design a road de-icing device by heating, we consider in a two dimensional setting the optimal control of an advection-diffusion equation with a nonlinear boundary condition of the Stefan-Boltzmann type. The problem models the heating of a road during a winter period to keep positive its surface temperature above a given threshold. The heating device is performed through the circulation of a coolant in a porous layer of the road. We prove the well-posedeness of the nonlinear optimal control problem, subjected to unilateral constraints, set up a gradient based algorithm then discuss some numerical results associated with real data obtained from experimental measurements. The study, initially developed in a one dimensional simpler setting in [1], aims to quantify the minimal energy to be provided to keep the road surface without frost or snow.

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hal-04686212 , version 1 (03-09-2024)

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  • HAL Id : hal-04686212 , version 1

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Frédéric Bernardin, Jerome Lemoine, Arnaud Munch. A non linear optimal control problem related to a road de-icing device: Analysis and Numerical experiments. 2024. ⟨hal-04686212⟩
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