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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Gruene_Schaller_Schiela_SensitivityAnalysisLQ_2018_preprint.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (311kB) 
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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 righthand 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.