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Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control

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. 2753-2774.
ISSN 0363-0129
DOI: https://doi.org/10.1137/18M1223083

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Official URL: Volltext

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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 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 right-hand 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 right-hand 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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: sensitivity analysis; turnpike property; model predictive control
Subject classification: Mathematics Subject Classification Code: 49K20, 49K40, 93D20
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 (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics) > Chair Applied Mathematics (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: 20 Aug 2019 05:47
Last Modified: 20 Aug 2019 05:47
URI: https://eref.uni-bayreuth.de/id/eprint/51929

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