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A Lyapunov function for economic MPC without terminal conditions

URN to cite this document: urn:nbn:de:bvb:703-epub-1982-5

Title data

Grüne, Lars ; Stieler, Marleen:
A Lyapunov function for economic MPC without terminal conditions.
Department of Mathematics, University of Bayreuth
Bayreuth , 2014 . - 6 S.

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Project information

Project title:
Project's official title
Project's id
SADCO - Sensitivity Analysis for Deterministic Controller Design
264735
Identifikation, Optimierung und Steuerung für technische Anwendungen
K-NW-2004-143
SPP 1305: Regelungstheorie digital vernetzter dynamischer Systeme
29058575
Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Elite Network of Bavaria
Deutsche Forschungsgemeinschaft
Marie-Curie Initial Training Network

Abstract

We consider nonlinear economic model predictive control (MPC) without terminal constraints or costs. We show that under suitable conditions, consisting of strict dissipativity, the turnpike property and appropriate continuity properties, a practical Lyapunov function exists for the MPC closed loop. This Lyapunov function is given by the optimal value function of the optimal control problem with rotated stage costs originating from the dissipativity condition. Alternative sufficient conditions in terms of suitable controllability properties and finite time optimality of the closed loop trajectories during the transient phase are also discussed.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen in:
Proceedings of the IEEE 53rd Annual Conference on Decision and Control Held in Los Angeles, California, 2014. - Los Angeles, CA, USA : Institute of Electrical and Electronics Engineers (IEEE) , 2014 . - S. 2740-2745
ISBN 978-1-4799-7746-8
DOI: https://doi.org/10.1109/CDC.2014.7039809


An extended paper containing results from Sections IV and V of this paper was submitted to the Journal of Process Control.
Keywords: economic MPC; Lyapunov function; dissipativity; turnpike property; stabilizability
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
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1982-5
Date Deposited: 02 Apr 2015 09:16
Last Modified: 16 Dec 2025 07:19
URI: https://epub.uni-bayreuth.de/id/eprint/1982
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