LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS WITH A TYPE OF RANDOM COEFFICIENTS

被引：0

作者：

Mei, Hongwei ^{[1
]}

Wei, Qingmeng ^{[2
]}

Yong, Jiongmin ^{[3
]}

机构：

[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

[2] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[3] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2024年 / 14卷 / 04期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Linear-quadratic control problem; mean-field; forward-backward stochastic differential equations; differential Riccati equation; open-loop solvability; closed-loop solvability;

D O I：

10.3934/naco.2024020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by linear-quadratic optimal control problems (LQ problems, for short) for mean-field stochastic differential equations (SDEs, for short) with the coefficients containing regime switching governed by a Markov chain, we consider an LQ problem for an SDE with the coefficients being adapted to a filtration independent of the Brownian motion driving the control system. Classical approach of completing the square is applied to the current problem and obvious shortcomings are indicated. Open-loop and closed-loop solvability are introduced and characterized.

引用

页码：813 / 852

页数：40

共 31 条

[1]

Anderson B. D. O., 1971, LINEAR OPTIMAL CONTR

[2] INVARIANT IMBEDDING AND THE REDUCTION OF 2-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS [J].

BELLMAN, R ;

KALABA, R ;

WING, GM .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1960, 46 (12) :1646-1649

[3]

Bellman R., 1958, Some Aspects Of the Mathematical Theory of Control Processes

[4]

Bensoussan A., 1981, NONLINEAR FILTERING, V972

[5] BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY CADLAG MARTINGALES [J].

Carbone, R. ;

Ferrario, B. ;

Santacroce, M. .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 2008, 52 (02) :304-314

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

Chen, SP ;

Li, XJ ;

Zhou, XY .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (05) :1685-1702

[7]

Davis M., 1977, Linear Estimation and Stochastic Control

[8] A LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE HORIZON [J].

Huang, Jianhui ;

Li, Xun ;

Yong, Jiongmin .

MATHEMATICAL CONTROL AND RELATED FIELDS, 2015, 5 (01) :97-139

[9]

Kalman R.E., 1960, Bol. Soc. Mat. Mex., V5, P102, DOI DOI 10.1109/9780470544334.CH8

[10] OPTIMAL STOCHASTIC CONTROL [J].

KUSHNER, HJ .

IRE TRANSACTIONS ON AUTOMATIC CONTROL, 1962, AC 7 (05) :120-&

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