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
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2019
. - 26 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 |
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Project financing: |
Deutsche Forschungsgemeinschaft Deutsche Forschungsgemeinschaft ARC (Australian Research Council) |
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 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
Available Versions of this Item
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Strict dissipativity for discrete time discounted optimal control problems. (deposited 07 Jun 2018 06:38)
- Strict dissipativity for discrete time discounted optimal control problems. (deposited 19 Sep 2019 06:54) [Currently Displayed]