Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control

Journal
SIAM journal on control and optimization  
Volume
63
Issue
2
Start Page
1432
End Page
1457
Citation
SIAM Journal on Control and Optimization 63 (2): 1432-1457 (2025)
Publisher DOI
10.1137/23M160089X
Scopus ID
2-s2.0-105007364884
Publisher
Soc.
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying dissipativity notion, we can conclude turnpike behaviors concerning different objects like distributions, moments, or sample paths of the stochastic system and that the distributions of the stationary pair can be characterized by a stationary optimization problem. The analytical findings are illustrated by numerical simulations.
Subjects
dissipativity | stochastic optimal control | stochastic systems | turnpike property
DDC Class
600: Technology