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Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity analysis of optimal control motivated by model predictive
control.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2018
. - 4 S.
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Project information
| Project title: |
Project's official title Project's id Specialized Adaptive Algorithms for Model Predictive Control of PDEs GR 1569/17-1 Specialized Adaptive Algorithms for Model Predictive Control of PDEs SCHI 1379/5-1 |
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| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
We analyze the sensitivity of the extremal equations that arise when concluding first order optimality conditions for time dependent optimization problems. More specifically, we consider parabolic PDEs with a linear quadratic performance criterion. We prove the solutions boundedness with respect to the right-hand side of the first order optimality condition which includes initial data. As a consequence, it can be shown that the influence of a perturbation at at certain time decays exponentially in the temporal distance to the time of perturbation. Moreover, a quantitative turnpike theorem can be derived.
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