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Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
In: Journal of Differential Equations. (28 November 2019) .
ISSN 0022-0396
DOI: https://doi.org/10.1016/j.jde.2019.11.064

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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 linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator. We show, that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the right-hand side including initial data with the bound being independent of the time horizon. Consequently, the influence of perturbations of the extremal equations decays exponentially in time. This property can for example be used to construct efficient space and time discretizations for a Model Predictive Control scheme. Furthermore, a turnpike property for unbounded but admissible control of general semigroups can be deduced.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: available online
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
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: 15 Jan 2020 07:11
Last Modified: 15 Jan 2020 07:11
URI: https://eref.uni-bayreuth.de/id/eprint/53733

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