## Title data

Schießl, Jonas ; Ou, Ruchuan ; Faulwasser, Timm ; Baumann, Michael Heinrich ; Grüne, Lars:

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

Bayreuth
,
2023

DOI: https://doi.org/10.48550/arXiv.2309.05422

## Project information

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

## Abstract in another language

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.