WIAS Preprint No. 639, (2001)

Suboptimal control of laser surface hardening using proper orthogonal decomposition



Authors

  • Hömberg, Dietmar
  • Volkwein, Stefan

2010 Mathematics Subject Classification

  • 35Kxx 49J20 49K20 65Nxx

Keywords

  • Laser hardening, optimality conditions, properorthogonal decomposition, error estimates, suboptimal control

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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