Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs.
Bayreuth
,
2020
. - 29 p.
Project information
Project title: |
Project's official title Project's id Specialized Adaptive Algorithms for Model Predictive Control of PDEs GR 1569/17-1 Specialized Adaptive Algorithms for Model Predictive Control of PDEs SCHI 1379/5-1 |
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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 two-dimensional domain.
Further data
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- Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. (deposited 08 Sep 2020 06:41) [Currently Displayed]