Abstract
In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed 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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Acknowledgements
This work was supported by the DFG project A-Posteriori-POD Error Estimators for Nonlinear Optimal Control Problems governed by Partial Differential Equations, grant VO 1658/2-1.
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Grimm, E., Gubisch, M., Volkwein, S. (2015). Numerical Analysis of Optimality-System POD for Constrained Optimal Control. In: Mehl, M., Bischoff, M., Schäfer, M. (eds) Recent Trends in Computational Engineering - CE2014. Lecture Notes in Computational Science and Engineering, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-22997-3_18
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