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Strict dissipativity for discrete time discounted optimal control problems

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00004841
URN to cite this document: urn:nbn:de:bvb:703-epub-4841-2

Title data

Grüne, Lars ; Müller, Matthias A. ; Kellett, Christopher M. ; Weller, Steven R.:
Strict dissipativity for discrete time discounted optimal control problems.
Bayreuth ; Stuttgart ; Canberra, Australia ; Newcastle, Australia , 2020 . - 29 S.

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Project information

Project title:
Project's official title
Project's id
Performance Analysis for Distributed and Multiobjective Model Predictive Control
Gr 1569/13-1
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov Functions
DP160102138
Project financing: Deutsche Forschungsgemeinschaft
ARC (Australian Research Council)t

Abstract

The paradigm of discounting future costs is a common feature of economic applications of optimal control. In this paper, we provide several results for such discounted optimal control aimed at replicating the now well-known results in the standard, undiscounted, setting whereby (strict) dissipativity, turnpike properties, and near-optimality of closed-loop systems using model predictive control are essentially equivalent. To that end, we introduce a notion of discounted strict dissipativity and show that this implies various properties including the existence of available storage functions, required supply functions, and robustness of optimal equilibria. Additionally, for discount factors sufficiently close to one we demonstrate that strict dissipativity implies discounted strict dissipativity and that optimally controlled systems, derived from a discounted cost function, yield practically asymptotically stable equilibria. Several examples are provided throughout.

Further data

Item Type: Preprint, postprint
Keywords: Dissipativity; Optimal Control; Discounting
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 > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Research Institutions
Research Institutions > Central research institutes
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4841-2
Date Deposited: 05 May 2020 08:35
Last Modified: 05 May 2020 08:41
URI: https://epub.uni-bayreuth.de/id/eprint/4841

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