Suboptimal control of laser surface hardening using proper orthogonal decomposition
- Hömberg, Dietmar
- Volkwein, Stefan
2010 Mathematics Subject Classification
- 35Kxx 49J20 49K20 65Nxx
- Laser hardening, optimality conditions, properorthogonal decomposition, error estimates, suboptimal control
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.
- 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.