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

URN to cite this document: urn:nbn:de:bvb:703-epub-4581-8

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 26 S.

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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
Project financing:	Deutsche Forschungsgemeinschaft

Abstract

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:	Preprint, postprint
Keywords:	Sensitivity Analysis; Turnpike Property; Model Predictive Control
Subject classification:	Mathematics Subject Classification Code: 49K20, 49K40, 93D20
DDC Subjects:	500 Science > 510 Mathematics
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
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-4581-8
Date Deposited:	14 Jan 2020 06:26
Last Modified:	14 Jan 2020 06:29
URI:	https://epub.uni-bayreuth.de/id/eprint/4581

Available Versions of this Item

Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. (deposited 13 Dec 2018 08:12)
- Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. (deposited 14 Jan 2020 06:26) [Currently Displayed]

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