Title data
Grüne, Lars ; Müller, Matthias A. ; Kellett, Christopher M. ; Weller, Steven R.:
Strict dissipativity for discrete time discounted optimal control problems.
In: Mathematical Control and Related Fields.
Vol. 11
(2021)
Issue 4
.
 pp. 771796.
ISSN 21568472
DOI: https://doi.org/10.3934/mcrf.2020046
This is the latest version of this item.
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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 1569/132 Activating LyapunovBased Feedback  Nonsmooth Control Lyapunov Functions DP160102138 

Project financing: 
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 wellknown results in the standard, undiscounted, setting whereby (strict) dissipativity, turnpike properties, and nearoptimality of closedloop 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.
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Available Versions of this Item

Strict dissipativity for discrete time discounted optimal control problems. (deposited 09 Jun 2018 21:00)

Strict dissipativity for discrete time discounted optimal control problems. (deposited 19 Sep 2019 06:54)

Strict dissipativity for discrete time discounted optimal control problems. (deposited 05 May 2020 08:40)
 Strict dissipativity for discrete time discounted optimal control problems. (deposited 23 Nov 2020 10:06) [Currently Displayed]

Strict dissipativity for discrete time discounted optimal control problems. (deposited 05 May 2020 08:40)

Strict dissipativity for discrete time discounted optimal control problems. (deposited 19 Sep 2019 06:54)