Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases

TL;DR

This paper extends the analysis of the turnpike property in large-horizon linear-quadratic optimal control problems to non-homogeneous systems with regime switching, revealing new insights even in simpler cases without switching.

Contribution

It generalizes previous results by establishing the turnpike property for non-homogeneous systems with regime switching, a case not previously addressed.

Findings

Established the strong turnpike property for non-homogeneous systems with regime switching

Extended the results to cases without regime switching, providing new insights

Demonstrated the applicability of the turnpike property in more complex stochastic control scenarios

Abstract

This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper \cite{Mei-Wang-Yong-2025}, in which the strong turnpike property was established for homogeneous linear systems with purely quadratic cost functionals. We extend the results to the current situation. It turns out that some of the results are new even for the cases without regime switchings.