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.

Format: PDF Name: LQ_dissipativity_turnpike.pdf Version: Preprint Available under License German copyright law. This contribution is freely accessible with the consent of the copyright holder on the basis of an (DFG-funded) alliance or national license. The document may be used free of charge for personal use. In addition, the reproduction, editing, distribution and any kind of exploitation require the written consent of the respective rights holder.

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Project information

Project title:	Project's official title Project'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
Additional notes (visible to public):	erschienen in: SIAM Journal on Control and Optimization. Bd. 56 (2018) Heft 2 . - S. 1282-1302. DOI: https://doi.org/10.1137/17M112350X
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 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:	27 May 2021 09:20
URI:	https://epub.uni-bayreuth.de/id/eprint/3261

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