Geodesic
An optimal control problem governed by the heat equation with nonconvex constraints applied to the selective laser melting process
Minimax theory and its applications, Tome 6 (2021) no. 2
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This paper deals with a PDE-constrained optimal control problem applied to an Additive Manufacturing process, namely a selective laser melting. Here, we want to control the temperature gradient inside the domain during a fixed time of heating, by acting on the trajectory of the dynamic Gaussian heating source. The nonconvex set of admissible controls reflects the fact that the control must fill the part of the boundary irradiated by the laser.
Mots-clés : Laser trajectory optimization, optimal control, non-convex constraints, first-order necessary optimality condition 
@article{MTA_2021_6_2_a1,
     author = {Tonia-Maria Alam and Serge Nicaise and Luc Paquet},
     title = {An optimal control problem governed by the heat equation with nonconvex constraints applied to the selective laser melting process},
     journal = {Minimax theory and its applications},
     year = {2021},
     volume = {6},
     number = {2},
     zbl = {1469.49006},
     url = {http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a1/}
}
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Tonia-Maria Alam; Serge Nicaise; Luc Paquet. An optimal control problem governed by the heat equation with nonconvex constraints applied to the selective laser melting process. Minimax theory and its applications, Tome 6 (2021) no. 2. http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a1/