Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition

Authors:
D. Hömberg;S. Volkwein
Affiliations:
Weierstrass-Institute for Applied Analysis and Stochastics Mohrenstrasse 39, D-10117 Berlin, Germany;Institut für Mathematik, Karl-Franzens-Universität Graz Heinrichstrasse 36, A-8010 Graz, Austria
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2003

Citing 7
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A posteriori error estimates for an optimal control problem of laser surface hardening of steel

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Abstract

Laser surface hardening of steel is formulated in terms of an optimal control problem, where the state equations are a semilinear heat equation and an ordinary differential equation, which describe the evolution of the high temperature phase. The optimal control problem is analyzed and first-order necessary optimality conditions are derived. An error estimate for POD (proper orthogonal decomposition) Galerkin methods for the state system is proved. Finally, a strategy to obtain suboptimal controls using POD is applied to solve some numerical examples.