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Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs

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.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Specialized Adaptive Algorithms for Model Predictive Control of PDEsGR 1569/17-1
Specialized Adaptive Algorithms for Model Predictive Control of PDEsSCHI 1379/5-1

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

Item Type: Preprint, postprint
Keywords: Nonlinear Optimal Control; Sensitivity Analysis; Turnpike Property; Model Predictive Control
Subject classification: Mathematics Subject Classification Code: 49K20, 49K40, 93D20, 35K55, 35Q93
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 08 Sep 2020 06:41
Last Modified: 08 Sep 2020 06:41
URI: https://eref.uni-bayreuth.de/id/eprint/56844