LQG量测反馈最优控制的精细积分

钟万勰; 蔡志勤

LQG量测反馈最优控制的精细积分

大连理工大学工业装备结构分析国家重点实验室, 大连116024

基金项目: 国家自然科学基金资助项目(19732020)

详细信息

作者简介:
钟万勰(1934- ),男,浙江德清人,教授,博士生导师,中国科学院院士;蔡志勤(1961- ),女,浙江宁波人,博士后,副教授.

中图分类号: O232
计量
- 文章访问数: 2394
- HTML全文浏览量: 124
- PDF下载量: 909
- 被引次数: 0
出版历程
- 收稿日期: 2000-02-22
- 刊出日期: 2000-12-15

Precise Integration Method for LQG Optimal Measurement Feedback Control Problem

State Key Laboratory of Structure Analysis, Dalian University of Technology, Dalian 116024, P R China

摘要

摘要: 对于线性二次型高斯(LQG)量测反馈最优控制问题,提出了精细积分解法。根据分离性原理,LQG控制问题可以分成为最优状态反馈控制问题以及最优状态估计问题,即:离线计算的两套黎卡提微分方程的求解以及状态向量的时变微分方程的在线积分解。该算法不仅适用于求解二点边值问题及其相应的黎卡提微分方程,也适用于求解状态估计的时变微分方程。精细积分高精度的特点,对控制和估计都是有利的。数值算例表明了算法的高精度及有效性。
- 精细积分 /
- LQG量测反馈控制 /
- 黎卡提(Riccati)微分方程 /
- 时变微分方程
Abstract: By using the precise integration method,the numerical solution of linear quadratic Gaussian(LQG)optimal control problem was discussed.Based on the separation principle,the LQG control problem decomposes,or separates,into an optimal state-feedback control problem and an optimal state estimation problem.That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation,but also can be used to solve the estimated state from the time-variant differential equations.The high precision of precise integration is of advantage for the control and estimation.Numerical examples demonstrate the high precision and effectiveness of the algorithm.
- precise integration /
- LQG measurement feedback control /
- Riccati differential equation /
- time-variant differential equation

HTML全文

参考文献(11)

[1]	郑大钟. 线性系统理论[M].北京:清华大学出版社,1990.
[2]	Green M, Limebeer D J N. Linear Robust Control[M]. Prentice-Hall,1995.
[3]	Meirovitch L. Dynamic and Control of Structures[M]. J Wiley & Sons,1990.
[4]	Doyal J C, Glover K, Khargoneker P P, et al. State space solutions to standard H₂ and H_∞ control problems[J]. IEEE Trans Automat Control,1989,34(8):831-847.
[5]	申铁龙. H_∞ 控制理论及应用[M]. 北京:清华大学出版社,1996.
[6]	钟万勰,等. 计算结构力学与最优控制[M]. 大连:大连理工大学出版社,1993.
[7]	钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社,1995.
[8]	钟万勰. 矩阵黎卡提方程的精细积分法[J]. 计算结构力学及其应用,1994,11(2):113-119.
[9]	钟万勰. 线性二次最优控制的精细积分法[J]. 自动化学报,2000,26(5).
[10]	钟万勰. 卡尔曼-布西滤波的精细积分[J]. 大连理工大学学报,1999, 39(2):191-200.
[11]	陆恺,田蔚风. 最优估计理论及其在导航中应用[M]. 上海:上海交通大学出版社,1990.