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Strict dissipativity for discrete time discounted optimal control problems

Title data

Grüne, Lars ; Müller, Matthias A. ; Kellett, Christopher M. ; Weller, Steven R.:
Strict dissipativity for discrete time discounted optimal control problems.
Bayreuth ; Stuttgart ; Newcastle, Australia , 2019 . - 26 p.

This is the latest version of this item.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Performance Analysis for Distributed and Multiobjective Model Predictive ControlGr 1569/13-1
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov FunctionsDP160102138

Project financing: Deutsche Forschungsgemeinschaft
Deutsche Forschungsgemeinschaft
ARC (Australian Research Council)

Abstract in another language

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 an appropriate available storage function 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
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Sep 2019 06:54
Last Modified: 19 Sep 2019 06:55
URI: https://eref.uni-bayreuth.de/id/eprint/52339

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