Turnpike properties for stochastic linear-quadratic optimal control problems with periodic coefficients

Sun，Jingrui1; Yong，Jiongmin2

2024-08-15

10.1016/j.jde.2024.04.012

Journal of Differential Equations   影响因子和分区

0022-0396

1090-2732

This paper is concerned with the turnpike property for a class of stochastic linear-quadratic (LQ, for short) optimal control problems with periodic coefficients. The stability and stabilizability of the control system are studied, followed by the discussion of the existence and uniqueness of periodic solutions. A deterministic periodic LQ problem is introduced and solved, whose optimal pair, together with a pair of correction processes, serves as the turnpike limit of the stochastic problem. It is shown that the turnpike limit is periodic in the distribution sense. In the special case of constant coefficients, the turnpike limit turns out to have stationary distributions, with the expectation being the solution to a static optimization problem.

Linear-quadratic Periodic Riccati equation Stabilizability Stochastic optimal control Turnpike property

SCI

英语

第一 ; 通讯

MATHEMATICS

2-s2.0-85190327220

Scopus

1.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
2.Department of Mathematics,University of Central Florida,Orlando,32816,United States

Sun，Jingrui,Yong，Jiongmin. Turnpike properties for stochastic linear-quadratic optimal control problems with periodic coefficients[J]. Journal of Differential Equations,2024,400:189-229.

Sun，Jingrui,&Yong，Jiongmin.(2024).Turnpike properties for stochastic linear-quadratic optimal control problems with periodic coefficients.Journal of Differential Equations,400,189-229.

Sun，Jingrui,et al."Turnpike properties for stochastic linear-quadratic optimal control problems with periodic coefficients".Journal of Differential Equations 400(2024):189-229.