当前位置: X-MOL 学术Optim. Control Appl. Methods › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A BSDE approach to stochastic linear quadratic control problem
Optimal Control Applications and Methods ( IF 1.8 ) Pub Date : 2021-02-04 , DOI: 10.1002/oca.2707
Wei Zhang 1 , Liangquan Zhang 1
Affiliation  

In this article, we study a kind of linear quadratic optimal control problem driven by forward–backward stochastic differential equations (FBSDEs in short) with deterministic coefficients. The cost functional is defined by the solution of FBSDEs. By means of the Girsanov transformation, the original issue is turned equivalently into the classical LQ problem. By functional analysis approach, some necessary and sufficient conditions for the existence of optimal controls have been obtained. Moreover, we investigate the relationship between two groups of first-order and second-order adjoint equations. A new stochastic Riccati equation is derived, which leads to the state feedback form of optimal control. By introducing a new Hamiltonian function with an exponential factor, we establish the stochastic maximum principle to deal with the stochastic linear quadratic problem for forward–backward stochastic system with nonconvex control domain using first-order adjoint equation. An illustrative example is given as well.

中文翻译:

随机线性二次控制问题的 BSDE 方法

在本文中,我们研究了一种由具有确定性系数的前向-后向随机微分方程(简称 FBSDE)驱动的线性二次最优控制问题。成本泛函由 FBSDE 的解决方案定义。通过 Girsanov 变换,原问题等价转化为经典的 LQ 问题。通过泛函分析的方法,得到了最优控制存在的一些充要条件。此外,我们研究了两组一阶和二阶伴随方程之间的关系。推导出一个新的随机Riccati方程,得到最优控制的状态反馈形式。通过引入一个新的具有指数因子的哈密顿函数,利用一阶伴随方程建立了随机最大值原理来处理具有非凸控制域的前向-后向随机系统的随机线性二次问题。还给出了说明性示例。
更新日期:2021-02-04
down
wechat
bug