On the Relationship Between Stochastic Turnpike and Dissipativity Notions

• 成果类型: Article
• 署名作者: Schiessl, Jonas; Baumann, Michael H.; Faulwasser, Timm; Gruene, Lars
• 署名单位: University of Bayreuth; Dortmund University of Technology; Hamburg University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3504352
• 发表日期: 2025
• 页码: 3527-3539
• 关键词: Optimal control; Stochastic processes; Random variables; trajectory; steady-state; Aerospace electronics; optimization; noise; measurement; COSTS; Dissipativity; stability of nonlinear systems; stochastic optimal control; Stochastic systems

摘要

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 $\mathit {L<^>{r}}$ 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 L & eacute;vy-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.