具有未知参数的LQG对偶控制算法研究

尚婷; 钱富才; 张晓艳; 谢国

doi:10.16383/j.aas.2017.c160401

具有未知参数的LQG对偶控制算法研究

doi: 10.16383/j.aas.2017.c160401

尚婷^1,,
钱富才^1,2, ,,
张晓艳^1,,
谢国^1,

1.
西安理工大学自动化与信息工程学院西安 710048
2.
西安工业大学陕西省自主系统与智能控制国际联合研究中心西安 710021

基金项目:

国家自然科学基金 61273127

陕西省科技攻关项目 2016GY-108

航天器在轨故障诊断与维修实验室开放课题 SDML_OF2015004

国家自然科学基金 U1534208

详细信息

作者简介:
尚婷   西安理工大学自动化与信息工程学院博士研究生.主要研究方向为最优控制, 随机控制, 系统辨识, 故障诊断.E-mail:tshang0722@126.com

张晓艳  西安理工大学自动化与信息工程学院博士研究生.主要研究方向为对偶控制, 最优控制, 故障诊断, 随机控制, 容错控制, 系统辨识.E-mail:xyzhang 2016@163.com

谢国  西安理工大学自动化与信息工程学院副教授.2013年获得日本大学工学博士学位.主要研究方向为轨道交通系统的安全性和可靠性, 最优控制, 和随机控制.E-mail:guoxie@xaut.edu.cn

通讯作者:
钱富才西安理工大学自动化与信息工程学院教授.主要研究方向为随机控制, 系统辨识, 非线性控制, 最优控制, 故障诊断和全球定位系统.本文通信作者.E-mail:qianfc@xaut.edu.cn

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出版历程
- 收稿日期: 2016-05-17
- 录用日期: 2017-03-30
- 刊出日期: 2017-08-20

Research on Dual Control Algorithm for LQG with Unknown Parameters

SHANG Ting^1
,,
QIAN Fu-Cai^{1,2
, ,},
ZHANG Xiao-Yan^1
,,
XIE Guo^1
,

1.
School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048
2.
The International Joint Research Center of Autonomous Systems and Intelligent Control, Xi'an Technological University, Xi'an 710021

Funds:

National Natural Science Foundation of China 61273127

Science and Technology Project of Shaanxi Province 2016GY-108

the Key Laboratory for Fault Diagnosis and Maintenance of Spacecraft in Orbit SDML_OF2015004

National Natural Science Foundation of China U1534208

More Information

Author Bio:
Ph. D. candidate at the School of Automation and Information Engineering, Xi'an University of Technology. Her research interest covers the optimal control, stochastic control, systems identification, fault diagnosis

Ph. D. candidate at the School of Automation and Information Engineering, Xi0an University of Technology. Her research interest covers dual control, optimal control, fault diagnosis, stochastic control, tolerant-fault control and system identiflcation

Associate professor at the School of Automation and Information Engineering, Xi0an University of Technology. He received his Ph. D. degree from Vihon University, Japan in 2013. His research interest covers safety and reliability of railway system, optimal control and stochastic control

Corresponding author: QIAN Fu-Cai Professor at the School of Automation and Information Engineering, Xi0an University of Technology. His research interest covers stochastic control, systems identiflcation, nonlinear control, optimal control, fault diagnosis and global positioning system. Corresponding author of this paper

摘要

摘要: 对于具有未知参数的LQG（Linear quadratic Gaussian）问题，提出了一种次优对偶控制方法，用Kalman滤波处理过程噪声和测量噪声，用前一时刻的后验概率对Cost-to-go进行线性近似，然后，用动态规划获得了次优控制律.最后，用一个例子说明了本文设计的控制器的实施过程.结果表明，该控制律具有良好的对偶性质，并能在学习和控制之间实现较好平衡.
- LQG (Linear quadratic Gaussian) /
- 动态规划 /
- 对偶控制 /
- 最优控制
Abstract: For the LQG problem with unknown parameters, a novel suboptimal dual control approach is proposed in this paper. First, Kalman filter is used to deal with the noises of process and measurement and posterior probabilities at the previous moment are used to linearly approximate the cost-to-go at the present moment. Then dynamic programming is adopted to obtain a suboptimal control law. Finally, an example is presented to illustrate the implementation process of the developed controller. The result shows that this control law has good dual property and achieves a better balance between learning and control.
- LQG (Linear quadratic Gaussian) /
- dynamic programming /
- dual control /
- optimal control
注释:

1) 本文责任编委方海涛

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图 1 后验概率演化

Fig. 1 The posterior probabilities evolving

下载: 全尺寸图片幻灯片

图 2 对偶控制与最优控制比较

Fig. 2 Comparision of the dual control with the optimal control

下载: 全尺寸图片幻灯片

表 1 不同不确定参数下Monte Carlo仿真性能指标比较

Table 1 Performance index of Monte Carlo runs comparison for different uncertainty parameters

最优控制	非对偶控制1	非对偶控制2	对偶控制
30.1702	5.1102×10⁵	379.9141	38.6375

下载: 导出CSV

表 2 两个控制律性能比较

Table 2 Performance comparison for two control laws in example

控制律	DUL控制	对偶控制
统计平均值	56.4350	39.2685
最大值	148.6953	126.3292
标准差	27.9879	21.2748

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