Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity Analysis of Optimal Control for a class of parabolic PDEs motivated by Model Predictive Control.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2018
.  23 S.
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parabolic_sensitivity_paper_preprint.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (367kB) 
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Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract
We analyze the sensitivity of the extremal equations that arise from the first order optimality conditions for time dependent optimization problems. More specifically, we consider parabolic PDEs with distributed or boundary control and a linear quadratic performance criterion. We prove the solution's boundedness with respect to the righthand side of the first order optimality condition which includes initial data. If the system fulfills a particular stabilizability and detectability assumption, the bound is independent of the time horizon. As a consequence, the influence of a perturbation of the righthand side at a certain time decreases exponentially backward in time. We use this property for the construction of efficient numerical discretizations in a Model Predictive Control scheme. Moreover, a quantitative turnpike theorem in the W([0,T])norm is derived.