Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs.
In: ESAIM : Control, Optimisation and Calculus of Variations.
Vol. 27
(2021)
.
 No. 56.
ISSN 12623377
DOI: https://doi.org/10.1051/cocv/2021030
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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 in another language
We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end, we present an abstract implicit function approach with scaled spaces. We will apply this abstract approach to problems governed by semilinear PDEs. In that context, we prove an exponential turnpike result and show that perturbations of the extremal equation's dynamics, e.g., discretization errors decay exponentially in time. The latter can be used for very efficient discretization schemes in a Model Predictive Controller, where only a part of the solution needs to be computed accurately. We showcase the theoretical results by means of two examples with a nonlinear heat equation on a twodimensional domain.
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Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. (deposited 08 Sep 2020 06:41)
 Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. (deposited 05 May 2021 09:52) [Currently Displayed]