Optimal control of a nonlinear thermal model for the design of a road de-icing device

Frédéric Bernardin (1) , Arnaud Munch (2, 3)

1 Cerema Direction Centre-Est - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Centre-Est
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

We consider in the one dimensional setting the optimal control of a parabolic equation with a non linear boundary condition of the Stefan-Boltzmann type. Both the punctual control and the corresponding state are subjected to a unilateral constraint. This control problem models the heating of a road during a winter period to keep the road surface temperature above a given threshold. The modeling is a first step of the modeling of a road heating device through the circulation of a coolant in a porous layer of the road. We first prove, under realistic physical assumptions, the well-posedeness of the control problem. We then perform some numerical experiments using real data obtained from experimental measurements. This models and the corresponding numerical results allow to quantify the minimal energy to be provided to keep the road surface without frost or snow.

Mots clés: Energy; Optimal control; Non linear parabolic equation; Road heating; Unilateral constraint; De-icing

Domaines: Optimisation et contrôle [math.OC]

Frédéric Bernardin, Arnaud Munch. Optimal control of a nonlinear thermal model for the design of a road de-icing device. 2018. ⟨hal-01731614v1⟩