| 带指数稳定度约束的不定随机LQ问题 |
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| 引用本文： | 马宏基,侯婷,邢建民.带指数稳定度约束的不定随机LQ问题[J].山东大学学报(理学版),2008,43(5):58-62. |
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| 作者姓名： | 马宏基 侯婷 邢建民 |
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| 作者单位： | 1. 山东科技大学理学院,山东,青岛,266510
2. 青岛科技大学数理学院,山东,青岛,266510 |
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| 摘 要： | 研究了一类带稳定度约束的无限时域不定随机LQ问题。目标是寻求既能使性能指标达到最小值,同时又能使状态具有不低于给定的均方收敛速度的最优控制。给出了问题良定的充分必要条件。通过一个广义代数Riccati方程的解的存在性给出了问题可达的一个充分条件。
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| 关 键 词： | 随机LQ问题 稳定度 良定性 可达性 |
| 文章编号： | 1671-9352(2008)05-0058-05 |
| 修稿时间： | 2007年10月8日 |
Indefinite stochastic LQ problem with exponential stability degree constraint |
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| MA Hong-ji,HOU Ting,XING Jian-min.Indefinite stochastic LQ problem with exponential stability degree constraint[J].Journal of Shandong University,2008,43(5):58-62. |
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| Authors: | MA Hong-ji HOU Ting XING Jian-min |
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| Institution: | 1. College of Science, Shandong University of Science and Technology, Qingdao 266510, Shandong, China；2. College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266510, Shandong, China |
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| Abstract: | An indefinite stochastic LQ problem was studied in an infinite time horizon with stability degree constraint. The objective was to find an optimal control, by which the cost function minimum and the state with the optimal control having a higher mean-square convergence rate can be obtained. First, a necessary and sufficient condition was provided for the well-posedness of this problem. Then, a sufficient condition for the attainability was obtained based on the solvability of a generalized algebraic Riccati equation. |
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| Keywords: | stochastic LQ problem stability degree well-posedness attainability |
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