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.

引用

页数：30

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