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On the relationship between stochastic turnpike and dissipativity notions

Title data

Schießl, Jonas ; Baumann, Michael Heinrich ; Faulwasser, Timm ; Grüne, Lars:
On the relationship between stochastic turnpike and dissipativity notions.
Bayreuth , 2023
DOI: https://doi.org/10.48550/arXiv.2311.07281

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Stochastic Optimal Control and MPC - Dissipativity, Risk, and Performance
499435839

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

In this paper, we introduce and study different dissipativity notions and different turnpike properties for discrete-time stochastic nonlinear optimal control problems. The proposed stochastic dissipativity notions extend the classic notion of Jan C. Willems to L^r random variables and to probability measures. Our stochastic turnpike properties range from a formulation for random variables via turnpike phenomena in probability and in probability measures to the turnpike property for the moments. Moreover, we investigate how different metrics (such as Wasserstein or Lévy-Prokhorov) can be leveraged in the analysis. Our results are built upon stationarity concepts in distribution and in random variables and on the formulation of the stochastic optimal control problem as a finite-horizon Markov decision process. We investigate how the proposed dissipativity notions connect to the various stochastic turnpike properties and we work out the link between these two different forms of dissipativity.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Stochastic Optimal Control; Stochastic Systems; Dissipativity; Stability of Nonlinear Systems
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 > Central research institutes
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 15 Nov 2023 07:50
Last Modified: 15 Nov 2023 07:50
URI: https://eref.uni-bayreuth.de/id/eprint/87746