Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2020
.  26 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 1569/171  Specialized Adaptive Algorithms for Model Predictive Control of PDEs  SCHI 1379/51 

Project financing: 
Deutsche Forschungsgemeinschaft

Abstract
We analyze the sensitivity of linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator. We show, that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the righthand side including initial data with the bound being independent of the time horizon. Consequently, the influence of perturbations of the extremal equations decays exponentially in time. This property can for example be used to construct efficient space and time discretizations for a Model Predictive Control scheme. Furthermore, a turnpike property for unbounded but admissible control of general semigroups can be deduced.
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