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POD a-posteriori error analysis for optimal control problems with mixed control-state constraints

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  • Martin Gubisch
  • Stefan Volkwein

Abstract

In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These problems arise when a Lavrentiev regularization is utilized for state constrained linear-quadratic optimal control problems. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. Numerical examples illustrate the theoretical results. In particular, the POD Galerkin scheme is applied to a problem with state constraints. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Martin Gubisch & Stefan Volkwein, 2014. "POD a-posteriori error analysis for optimal control problems with mixed control-state constraints," Computational Optimization and Applications, Springer, vol. 58(3), pages 619-644, July.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:3:p:619-644
    DOI: 10.1007/s10589-014-9636-1
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    References listed on IDEAS

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    1. F. Tröltzsch & S. Volkwein, 2009. "POD a-posteriori error estimates for linear-quadratic optimal control problems," Computational Optimization and Applications, Springer, vol. 44(1), pages 83-115, October.
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