Forward-backward linear quadratic stochastic optimal control problem with delay

被引：47

作者：

Huang, Jianhui ^{[2
]}

Li, Xun ^{[2
]}

Shi, Jingtao ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

SYSTEMS & CONTROL LETTERS | 2012年 / 61卷 / 05期

基金：

中国博士后科学基金;

关键词：

Stochastic optimal control; Stochastic differential delayed equation; Anticipated backward stochastic differential equation; Stochastic delayed system; Linear quadratic control; Time-inconsistent; DIFFERENTIAL-EQUATIONS; PRINCIPLE;

D O I：

10.1016/j.sysconle.2012.02.010

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with one kind of forward-backward linear quadratic stochastic control problem whose system is described by a linear anticipated forward-backward stochastic differential delayed equation. The explicit form of the optimal control is derived. Optimal state feedback regulators are studied in two special cases. For the case with delay in just the control variable, the optimal state feedback regulator is obtained by the Riccati equation. For the other case with delay in just the state variable, the optimal state feedback regulator is analyzed by the value function approach.

引用

页码：623 / 630

页数：8

共 25 条

[1] QUADRATIC PROBLEM FOR SYSTEMS WITH TIME DELAYS [J].

ALEKAL, Y ;

BRUNOVSKY, P ;

CHYUNG, DH ;

LEE, EB .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1971, AC16 (06) :673-+

[2] Necessary and sufficient conditions for near-optimality in stochastic control of FBSDEs [J].

Bahlali, Khaled ;

Khelfallah, Nabil ;

Mezerdi, Brahim .

SYSTEMS & CONTROL LETTERS, 2009, 58 (12) :857-864

[3]

Chen L, 2011, CHIN CONTR CONF, P1344

[4] A type of general forward-backward stochastic differential equations and applications [J].

Chen, Li ;

Wu, Zhen .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2011, 32 (02) :279-292

[5] Maximum principle for the stochastic optimal control problem with delay and application [J].

Chen, Li ;

Wu, Zhen .

AUTOMATICA, 2010, 46 (06) :1074-1080

[6] Stochastic linear quadratic regulators with indefinite control weight costs. II [J].

Chen, SP ;

Zhou, XY .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 39 (04) :1065-1081

[7]

Cvitanic J, 1996, ANN APPL PROBAB, V6, P370

[8]

Doluchaev N, 1999, J MATH ANAL APPL, V238, P143

[9]

Kolmanovskii VB., 1973, Avtomat. i Telemeh, V1, P47

[10]

Kolmanovsky V.B., 1996, T MATH MONOGRAPHS, V157

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