| 线性二次最优控制的精细积分法 |
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| 引用本文： | 钟万勰.线性二次最优控制的精细积分法[J].自动化学报,2001,27(2):166-173. |
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| 作者姓名： | 钟万勰 |
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| 作者单位： | 1.大连理工大学工业装备结构分析国家重点实验室,大连 |
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| 摘 要： | LQ控制虽然是最优控制的最基本问题,但其数值求解仍有很多问题.黎卡提微分
方程的精细积分法利用黎卡提方程的解析特点,求出计算机上高度精密的解,并已证明误差
在计算机倍精度数的误差范围之外.这对于Kalman-Bucy滤波,LQG问题以及H∞控制及滤
波等都可运用,精细积分还求解了反馈后的状态微分方程.数例验证了其高精度特性.
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| 关 键 词： | LQ控制 黎卡提方程 精细积分 |
| 收稿时间： | 1998-7-20 |
| 修稿时间： | 1998年7月20日 |
The Precise Integration of LQ Control Problems |
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| ZHONG Wan-xie.The Precise Integration of LQ Control Problems[J].Acta Automatica Sinica,2001,27(2):166-173. |
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| Authors: | ZHONG Wan-xie |
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| Affiliation: | 1.State Key Lab of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian |
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| Abstract: | Linear quadratic control is one of the basic problems for optimal control, however, its numerical computations still have to be solved. The precise integration of the Riccati matrix differential equations introduced in this paper is very attractive. The analytic characteristics of the Riccati equation is applied to deriving the high precision numerical solution so that the full computer precision is reached. The same method can also be applied to such as Kalman-Bucy filtering, LQG and H∞ control problems. The precise integration method differs from the usual finite difference style method dramatically, and the numerical examples verify the high precision of the solutions. The state vector equation under optimal control is also solved by the precise integration method. |
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| Keywords: | LQ control Riccati equation precise integration |
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