Pathwise turnpike and dissipativity results for discrete-time stochastic linear-quadratic optimal control problems

TL;DR

This paper explores the pathwise turnpike phenomenon in discrete-time stochastic LQ control problems, introducing a new dissipativity concept that uses stationary stochastic processes instead of deterministic steady states.

Contribution

It presents a novel strict dissipativity framework for stochastic LQ problems, extending the understanding of turnpike behavior in stochastic control.

Findings

Pathwise turnpike behavior demonstrated in stochastic LQ problems

Introduction of a new dissipativity notion involving stationary stochastic processes

Numerical example illustrating theoretical results

Abstract

We investigate pathwise turnpike behavior of 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. The analytical findings are illustrated by a numerical example.