带指数稳定度约束的不定随机LQ问题

J4 ›› 2008, Vol. 43 ›› Issue (5): 58-62 .doi:

带指数稳定度约束的不定随机LQ问题

马宏基¹,侯婷¹,邢建民²

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

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 马宏基

Indefinite stochastic LQ problem with exponential stability degree constraint

MA Hong-ji¹, HOU Ting¹, XING Jian-min²

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

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: MA Hong-ji

摘要/Abstract

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。

关键词: 随机LQ问题;稳定度;良定性;可达性

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.

Key words: stochastic LQ problem; stability degree; well-posedness; attainability

中图分类号:

O231.3

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]. J4, 2008, 43(5): 58-62 .

MA Hong-ji,HOU Ting,XING Jian-min . Indefinite stochastic LQ problem with exponential stability degree constraint[J]. J4, 2008, 43(5): 58-62 .

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed