WIAS Preprint No. 639, (2001)
Suboptimal control of laser surface hardening using proper orthogonal decomposition
Authors
- Hömberg, Dietmar
ORCID: 0000-0001-9460-5729 - Volkwein, Stefan
2010 Mathematics Subject Classification
- 35Kxx 49J20 49K20 65Nxx
Keywords
- Laser hardening, optimality conditions, properorthogonal decomposition, error estimates, suboptimal control
DOI
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 describes 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 developed and validated by computing some numerical examples.
Appeared in
- Math. Comput. Modelling, 37 (2003), pp. 1003-1028 under new title: Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition.
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