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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

Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)

264735-SADCO

International Doctorate Program "Identification, Optimization and Control with Applications in Modern Technologies"

K-NW-2004-143

DFG Priority Program 1305 "Control theory for digitally networked dynamical systems", DFG Project "Performance Analysis for Distributed and Multiobjective Model Predictive Control"

GR 1569/13-1

Project financing:

7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Elite Network of Bavaria, Deutsche Forschungsgemeinschaft

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:	01 Jun 2021 09:39
URI:	https://epub.uni-bayreuth.de/id/eprint/1982

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