An optimal control problem governed by heat equation with nonconvex constraints applied to selective laser melting process

Tonia-Maria Alam (1) , Serge Nicaise (1) , Luc Paquet (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

This paper deals with a PDE-constraints 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 non convex 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

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Tonia-Maria Alam, Serge Nicaise, Luc Paquet. An optimal control problem governed by heat equation with nonconvex constraints applied to selective laser melting process. Minimax Theory and its Applications, 2021, 6 (2), pp.191-204. ⟨hal-02302403⟩