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Local turnpike analysis using local dissipativity for discrete time discounted optimal control

Title data

Grüne, Lars ; Krügel, Lisa:
Local turnpike analysis using local dissipativity for discrete time discounted optimal control.
In: Applied Mathematics and Optimization. Vol. 84 (2021) Issue Suppl. 2 . - pp. 1585-1606.
ISSN 1432-0606
DOI: https://doi.org/10.1007/s00245-021-09805-4

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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 1569/13-2

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with discounted stage cost are of great interest. In contrast to non-discounted optimal control problems, it is more likely that several asymptotically stable optimal equilibria coexist. Due to the discounting and transition cost from a local to the global equilibrium, it may be more favourable staying in a local equilibrium than moving to the global - cheaper - equilibrium. In the literature, strict dissipativity was shown to provide criteria for global asymptotic stability of optimal equilibria and turnpike behavior. In this paper, we propose a local notion of discounted strict dissipativity and a local turnpike property, both depending on the discount factor. Using these concepts, we investigate the local behaviour of (near-)optimal trajectories and develop conditions on the discount factor to ensure convergence to a local asymptotically stable optimal equilibrium.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Discounted Optimal Control; Dissipativity; Turnpike
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
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 01 Sep 2021 10:16
Last Modified: 24 Oct 2022 05:20
URI: https://eref.uni-bayreuth.de/id/eprint/66893

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