Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Levy Process

Huang Hong; Wang Xiangrong; Hou Ting; Xu Lu

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Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Levy Process

机译：与征税过程相关的前向后向随机控制系统的线性二次随机最优控制

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This paper analyzes one kind of linear quadratic (LQ) stochastic control problem of forward backward stochastic control system associated with Levy process. We obtain the explicit form of the optimal control, then prove it to be unique, and get the linear feedback regulator by introducing one kind of generalized Riccati equation. Finally, we discuss the solvability of the generalized Riccati equation, and its existence and uniqueness of the solutions are proved in a special case.

机译：本文分析了与Levy过程相关的前向后向随机控制系统的一种线性二次（LQ）随机控制问题。我们得到最优控制的显式形式，然后证明它是唯一的，并通过引入一种广义的Riccati方程得到线性反馈调节器。最后，我们讨论了广义Riccati方程的可解性，并在特殊情况下证明了其存在性和解的唯一性。

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来源
《Mathematical Problems in Engineering》 |2017年第9期|2541687.1-2541687.11|共11页
作者
Huang Hong; Wang Xiangrong; Hou Ting; Xu Lu;
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Shandong Univ Sci & Technol, Inst Financial Engn, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Inst Financial Engn, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China;

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1. General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations [J] . Tang SJ. SIAM Journal on Control and Optimization . 2003,第1期

机译：具有随机系数的一般线性二次最优随机控制问题：线性随机Hamilton系统和后向随机Riccati方程
2. An Indefinite Stochastic Linear Quadratic Optimal Control Problem with Delay and Related Forward–Backward Stochastic Differential Equations [J] . Na Li, Yuan Wang, Zhen Wu Journal of Optimization Theory and Applications . 2018,第2期

机译：延迟和相关前后随机微分方程的无限期随机线性二次最优控制问题
3. FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES [J] . WU Zhen Journal of Systems Science and Complexity . 2005,第2期

机译：前向-随机微分方程，线性二次随机最优控制和零和和微分游戏
4. LQ Stochastic Optimal Control of Forward-Backward Stochastic Control System Driven by Levy Process [C] . Hong Huang, Xiangrong Wang IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference . 2016

机译：征收过程驱动前后随机控制系统的LQ随机优化控制
5. Stochastic indefinite linear-quadratic optimal control. [D] . Chen, Xi. 2000

机译：随机不定线性二次最优控制。
6. Heat Shock Response in CHO Mammalian Cells Is Controlled by a Nonlinear Stochastic Process [O] . Ovidiu Lipan, Jean-Marc Navenot, Zixuan Wang, 2007

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7. Forward-backward linear quadratic stochastic optimal control problem with delay [O] . Huang J, Li X, Shi J 2012

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Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Levy Process

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