| 线性随机系统的最优反馈控制及拟Riccati方程的解 |
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| 引用本文： | 朱岚,周渊.线性随机系统的最优反馈控制及拟Riccati方程的解[J].复旦学报(自然科学版),2009(6). |
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| 作者姓名： | 朱岚 周渊 |
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| 作者单位： | 复旦大学数学科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10571030;10971127); 国家重点基础研究发展规划(973计划)资助项目(2007CB814904) |
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| 摘 要： | 主要研究了多维线性随机系统在非二次的目标泛函下的最优控制问题,给出了最优闭环控制以及系统对应的拟Riccati方程的表达式,讨论了特殊情况下的拟Riccati方程的经典解的存在惟一性,最后还求出了一类拟Riccati方程的经典解并通过求解拟Riccati方程得到了最优投资组合的解.
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| 关 键 词： | 随机最优控制 非二次指标 拟Riccati方程 正倒向随机微分方程组 |
The Optimal Feedback Control of Linear Stochastic Systems and the Solutions of Quasi-Riccati Equations |
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| ZHU Lan,ZHOU Yuan.The Optimal Feedback Control of Linear Stochastic Systems and the Solutions of Quasi-Riccati Equations[J].Journal of Fudan University(Natural Science),2009(6). |
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| Authors: | ZHU Lan ZHOU Yuan |
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| Institution: | ZHU Lan,ZHOU Yuan(School of Mathematical Sciences,Fudan University,Shanghai 200433,China) |
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| Abstract: | The optimal control problem for multidimensional linear stochastic systems with non-quadratic cost function is studied.Optimal feed-back controls are formulated via the related quasi-Riccati equation.Sufficient conditions for the existence of the quasi-Riccati equation are proved with the help of forward-backward stochastic differential equation.The explicit solution for a class of quasi-Riccati equations are given to solve a kind of optimal portfolio problem. |
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| Keywords: | stochastic optimal control non-quadratic performance quasi-Riccati equation forward-backward stochastic equation |
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