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Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems

URN to cite this document: urn:nbn:de:bvb:703-epub-3261-6

Title data

Grüne, Lars ; Guglielmi, Roberto:
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems.
Bayreuth , 2017 . - 20 S.

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LQ_dissipativity_turnpike.pdf - Preprint
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Project information

Project title:
Project's official titleProject's id
DFG-Project "Performance Analysis for Distributed and Multiobjective Model Predictive Control"GR 1569/13-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract

We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linear-quadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict pre-dissipativity of a system at an equilibrium point and link these properties to the turnpike behaviour of the optimal control problem. Moreover, we give further conditions to ensure that the turnpike behavior is of exponential type, i.e., the optimal trajectories are exponentially close to a steady-state of the system for all but finitely many time instants whose number is bounded independently of the optimization horizon.

Further data

Item Type: Preprint, postprint
Keywords: turnpike property; linear-quadratic optimal control; dissipativity; detectabil-
ity; Lyapunov matrix inequality; long time behaviour
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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)
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)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions
Research Institutions > Research Centres
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3261-6
Date Deposited: 31 Mar 2017 12:29
Last Modified: 28 Mar 2019 10:33
URI: https://epub.uni-bayreuth.de/id/eprint/3261

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