Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems  

作　　者：Jingrui SUN Hanxiao WANG Jiongmin YONG 

机构地区：[1]Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,China [2]Corresponding author.College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China [3]Department of Mathematics,University of Central Florida,Orlando,FL 32816,USA

出　　处：《Chinese Annals of Mathematics,Series B》2022年第6期999-1022,共24页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11901280,12271242,12201424);Guangdong Basic and Applied Basic Research Foundation(No.2021A1515010031);Shenzhen Fundamental Research General Program(No.JCYJ20220530112814032);NSF(No.DMS-1812921)。

摘　　要：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.

关 键 词：Turnpike property Stochastic optimal control Static optimization Linear-quadratic STABILIZABILITY Riccati equation 

分 类 号：O232[理学—运筹学与控制论]