General linear forward and backward Stochastic difference equations with applications
General linear forward and backward Stochastic difference equations with applications
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一般线性正向和反向随机差分方程及其应用
DOI：
10.1016/j.automatica.2018.06.031
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发表时间：
2018
期刊：
影响因子：
6.4
通讯作者：
Lihua Xie
中科院分区：
文献类型：
--
作者：
Juanjuan Xu;Huanshui Zhang;Lihua Xie
本文考虑了一类一般的线性正倒向随机差分方程。利用Riccati方程给出了FBSDES（唯一）解存在的充分必要条件。作为应用，研究了两类随机LQ最优控制问题。首先，我们推导出最优解的经典随机LQ问题的解决方案，应用到相关的FBSDES。其次，我们研究了一类由正倒向随机系统（FBSS）控制的新型LQ问题。将极大值原理和解应用于倒向随机微分方程，给出了一个以Riccati方程表示的显式解。最后，通过研究Riccati方程的渐近性态，得到了FBSS均方能镇定的一个等价条件。
In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS.