On the relationship between stochastic turnpike and dissipativity notions

Journal
IEEE transactions on automatic control  
Volume
70
Issue
6
Start Page
3527
End Page
3539
Citation
IEEE Transactions on Automatic Control 70 (6): 3527-3539 (2025)
Publisher DOI
10.1109/TAC.2024.3504352
Scopus ID
2-s2.0-85210384501
Publisher
IEEE
In this article, 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 LR 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 different forms of dissipativity.
Subjects
Dissipativity
stability of nonlinear systems
stochastic optimal control
stochastic systems
DDC Class
600: Technology
510: Mathematics