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Sensitivity analysis of optimal control motivated by model predictive control

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity analysis of optimal control motivated by model predictive control.
Department of Mathematics, University of Bayreuth
Bayreuth , 2018 . - 4 p.

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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 when concluding first order optimality conditions for time dependent optimization problems. More specifically, we consider parabolic PDEs with a linear quadratic performance criterion. We prove the solutions boundedness with respect to the right-hand side of the first order optimality condition which includes initial data. As a consequence, it can be shown that the influence of a perturbation at at certain time decays exponentially in the temporal distance to the time of perturbation. Moreover, a quantitative turnpike theorem can be derived.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
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 > Professorship Applied Mathematics (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship 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: 17 Feb 2018 22:00
Last Modified: 15 Aug 2018 06:30
URI: https://eref.uni-bayreuth.de/id/eprint/42304

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