General indefinite backward stochastic linear-quadratic optimal control problems

被引:2
作者
Sun, Jingrui [1 ]
Wen, Jiaqiang [1 ]
Xiong, Jie [1 ,2 ]
机构
[1] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
[2] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China
基金
中国国家自然科学基金;
关键词
Backward stochastic differential equation; linear-quadratic; optimal control; Riccati equation; nonhomo-geneous term; EQUATION; GAME;
D O I
10.1051/cocv/2022030
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite, and the cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly.
引用
收藏
页数:17
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