由Lévy过程驱动的随机线性二次最优控制问题  

Stochastic Linear Quadratic Optimal Control Problem Driven by Lévy Process

作　　者：武灿文 唐矛宁[2] WU Canwen;TANG Maoning(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China;School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2021年第8期6-17,共12页Journal of Huzhou University

基　　金：国家自然科学基金项目(11871121);浙江省自然科学基金项目(LY21A010001)。

摘　　要：主要研究一类在更一般情况下的随机线性二次最优控制问题.该系统由Teugel’s鞅和布朗运动共同驱动,且状态方程中存在漂移项,性能指标中含有交叉项.研究中基于凸变分原理得到最优控制的存在唯一性;利用对偶技术导出最优控制的对偶表达式,建立随机Hamiltonian系统,该系统是一个含有Teugel’s鞅的、线性的、完全耦合的正倒向随机微分方程;通过随机Hamiltonian系统推导出相应的Riccati方程,并通过证明Riccati方程解的存在唯一性获得了最优控制的反馈表达式.In this paper, we study a class of stochastic linear quadratic optimal control problems in more general cases.There are drift terms in the state equation and cross terms in the cost functional, and the system is driven by Teugel’s martingales and Brownian motion. Based on the convex variational principle, the existence and uniqueness of optimal control are obtained firstly. Secondly, the dual representation of the optimal control is derived by using the dual technique, and the stochastic Hamiltonian system is established. The system is a linear coupled forward-backward stochastic differential equation with Teugel’s martingales. Then the corresponding Riccati equation is derived by the stochastic Hamiltonian system. Finally, by proving the existence and uniqueness of the solution of Riccati equation, the feedback expression of optimal control is obtained.

关 键 词：Teugel’s鞅 随机线性二次最优控制 反馈表示 随机Hamiltonian系统 RICCATI方程 

分 类 号：O413[理学—理论物理]