Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems

被引：1
|
作者：
Sun, Jingrui [1 ,2 ]
Wu, Zhen [3 ]
Xiong, Jie [1 ,2 ]
机构：
[1] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
[2] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China
[3] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷
基金：
国家重点研发计划;
关键词：
Indefinite; backward stochastic differential equation; linear-quadratic; optimal control; Riccati equation; DIFFERENTIAL-EQUATION; OPEN-LOOP; REGULATORS; GAME;
D O I：
10.1051/cocv/2023033
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 a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state processes are presented in the cost functional. Based on a Hilbert space method, necessary and sufficient conditions are derived for the solvability of the problem, and a general approach for constructing optimal controls is developed. The crucial step in this construction is to establish the solvability of a Riccati-type equation, which is accomplished under a fairly weak condition by investigating the connection with forward stochastic LQ optimal control problems.
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页数：30
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