ON AN OPTIMAL CONTROL PROBLEM IN LASER CUTTING WITH MIXED FINITE-/INFINITE-DIMENSIONAL CONSTRAINTS

摘要

A mathematical model for laser cutting with time-dependent cutting velocity is presented. The model involves two coupled nonlinear partial differential equations for the interacting dynamical behaviors of the free melt boundaries during the process. We define a measurement for the roughness of a cutting surface and introduce an optimal control problem for minimizing the roughness with respect to the cutting velocity and the laser beam intensity along the free melt surface. The optimal control problem involves an additional finite-dimensional averaging constraint. Necessary optimality conditions will be deduced and illustrated by means of numerical examples with data from industrial applications.