Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases

2025/06/11 by Mei, Hongwei, Wang, Rui, Yong, Jiongmin · 3 citations
#49N10 #93E15 #93E20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2506.09337

Abstract

This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to those in the previous literature, which also provides a new tool for further research.

Citations

• Ergodicity and turnpike properties of linear-quadratic mean field control problems
• Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching
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• On the Turnpike Property and the Receding-Horizon Method for\n Linear-Quadratic Optimal Control Problems
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• The turnpike property in finite-dimensional nonlinear optimal control
• A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon
• A Mathematical Theory of Saving
• Stability of stochastic differential equations with Markovian switching

Cited by

• Turnpike Property of Mean-Field Linear-Quadratic Optimal Control Problems in Infinite-Horizon with Regime Switching
• Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
• Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases

Related

• Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases
• Turnpike Property of Mean-Field Linear-Quadratic Optimal Control Problems in Infinite-Horizon with Regime Switching
• Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems
• Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems
• Stochastic linear-quadratic optimal control problems with multi-dimensional state and non-Markovian regime switching