Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control.
In: SIAM Journal on Control and Optimization.
Vol. 57
(6 August 2019)
Issue 4
.
 pp. 27532774.
ISSN 03630129
DOI: https://doi.org/10.1137/18M1223083
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Deutsche Forschungsgemeinschaft 
Abstract in another language
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 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.
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Sensitivity Analysis of Optimal Control for a class of parabolic PDEs motivated by Model Predictive Control. (deposited 27 Oct 2018 21:00)
 Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control. (deposited 20 Aug 2019 05:47) [Currently Displayed]