Minimax Theory and its Applications 06 (2021), No. 2, 191--204
Copyright Heldermann Verlag 2021
An Optimal Control Problem Governed by the Heat Equation with Nonconvex Constraints Applied to the Selective Laser Melting Process
Tonia-Maria Alam
Université Polytechnique Hauts-de-France, LAMAV -- FR CNRS 2956, 59313 Valenciennes, France
ToniaMaria.Alam@uphf.fr
Serge Nicaise
Université Polytechnique Hauts-de-France, LAMAV -- FR CNRS 2956, 59313 Valenciennes, France
Serge.Nicaise@uphf.fr
Luc Paquet
Université Polytechnique Hauts-de-France, LAMAV -- FR CNRS 2956, 59313 Valenciennes, France
Luc.Paquet@uphf.fr
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.
Keywords: Laser trajectory optimization, optimal control, non-convex constraints, first-order necessary optimality condition.
MSC: 49B22, 74F05.
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