Numerical Analysis of Optimality-System POD for Constrained Optimal Control

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In this work linear-quadratic optimal control problems for parabolic equa- tions with control and state constraints are considered. Utilizing a Lavrentiev regu- larization we obtain a linear-quadratic optimal control problem with mixed control- state constraints. For the numerical solution a Galerkin discretization is applied uti- lizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, com- puted on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.

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ISO 690GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control
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@unpublished{Grimm2015Numer-30103,
  year={2015},
  title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control},
  author={Grimm, Eva and Gubisch, Martin and Volkwein, Stefan},
  note={Beitrag wird veröffentlicht in "Lecture Notes in Computational Science and Engineering"}
}
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Beitrag wird veröffentlicht in "Lecture Notes in Computational Science and Engineering"
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