| 一类带随机跳跃的完全耦合的线性二次随机控制问题 |
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| 引用本文： | 史敬涛, 吴臻. 一类带随机跳跃的完全耦合的线性二次随机控制问题. 自动化学报, 2009, 35(1): 92-97. doi: 10.3724/SP.J.1004.2009.00092 |
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| 作者姓名： | 史敬涛 吴臻 |
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| 作者单位： | 1.山东大学数学学院 济南 250100 |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国家自然科学基金，山东省自然科学基金 |
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| 摘 要： | 研究一类带随机跳跃的完全耦合的线性二次随机控制问题. 得到了最优控制的显式解, 并可以证明最优控制是唯一的. 引入了一类推广的黎卡提方程并讨论了其可解性. 利用这一类推广的黎卡提方程的解, 得到了上述带随机跳跃的最优控制问题的线性状态反馈调节器.
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| 关 键 词： | 倒向随机微分方程 泊松过程 线性二次随机控制 黎卡提方程 |
| 收稿时间： | 2007-07-04 |
| 修稿时间： | 2008-01-06 |
One Kind of Fully Coupled Linear Quadratic Stochastic Control Problem with Random Jumps |
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| SHI Jing-Tao, WU Zhen. One Kind of Fully Coupled Linear Quadratic Stochastic Control Problem with Random Jumps. ACTA AUTOMATICA SINICA, 2009, 35(1): 92-97. doi: 10.3724/SP.J.1004.2009.00092 |
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| Authors: | SHI Jing-Tao WU Zhen |
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| Affiliation: | 1. School of Mathematics, Shandong University, Jinan 250100, P.R.China |
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| Abstract: | One kind of fully coupled linear quadratic stochas-tic control problem with random jumps is studied. The explicit form of the optimal control is obtained. The optimal control can be proved to be unique. One kind of generalized Riccati equa-tion system is introduced and its solvability is discussed. The linear feedback regulator for the optimal control problem with random jumps is given by the solution of the generalized Riccati equation system. |
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| Keywords: | Backward stochastic differential equation pois-son process linear quadratic stochastic control Riccati equation |
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