Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems

Sun，Jiangrui1; Wang，Hanxiao2; Yong，Jiongmin3

2022-11-01

10.1007/s11401-022-0374-x

CHINESE ANNALS OF MATHEMATICS SERIES B   Impact Factor & Quartile

0252-9599

1860-6261

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon [0, T] as T → ∞. The so-called turnpike properties are established for such problems, under stabilizability condition which is weaker than the controllability, normally imposed in the similar problem for ordinary differential systems. In dealing with the turnpike problem, a crucial issue is to determine the corresponding static optimization problem. Intuitively mimicking the deterministic situations, it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem. However, this would lead us to a wrong direction. It is found that the correct static problem should contain the diffusion as a part of the objective function, which reveals a deep feature of the stochastic turnpike problem.

49N10 93D23 93E15 93E20 Linear-quadratic Riccati equation Stabilizability Static optimization Stochastic optimal control Turnpike property

English

First

MATHEMATICS

2-s2.0-85143349993

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
2.College of Mathematics and Statistics,Shenzhen University,Shenzhen,518060,China
3.Department of Mathematics,University of Central Florida,Orlando,32816,United States

Sun，Jiangrui,Wang，Hanxiao,Yong，Jiongmin. Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems[J]. CHINESE ANNALS OF MATHEMATICS SERIES B,2022,43(6):999-1022.

Sun，Jiangrui,Wang，Hanxiao,&Yong，Jiongmin.(2022).Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems.CHINESE ANNALS OF MATHEMATICS SERIES B,43(6),999-1022.

Sun，Jiangrui,et al."Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems".CHINESE ANNALS OF MATHEMATICS SERIES B 43.6(2022):999-1022.