Abstract
In this paper a linear-quadratic optimal control problem governed by a parabolic equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. In this paper the authors focus on testing the a-posteriori estimate’s validity by means of numerical examples. An intensive study of the consequences of certain choices that can be made within the POD basis determination process is carried out and the findings are discussed.
The second author gratefully acknowledges support by the German Science Fund DFG grant VO 1658/2-1 A-posteriori-POD Error Estimators for Nonlinear Optimal Control Problems governed by Partial Differential Equations.
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Studinger, A., Volkwein, S. (2013). Numerical Analysis of POD A-posteriori Error Estimation for Optimal Control. In: Bredies, K., Clason, C., Kunisch, K., von Winckel, G. (eds) Control and Optimization with PDE Constraints. International Series of Numerical Mathematics, vol 164. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0631-2_8
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DOI: https://doi.org/10.1007/978-3-0348-0631-2_8
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