• 论文 •

### 基于随机与区间分析的状态方程不确定性比较

1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083
• 收稿日期:2016-01-06 出版日期:2017-01-20 发布日期:2016-05-23
• 通讯作者: 李清东,E-mail:liqingdong@buaa.edu.cn E-mail:liqingdong@buaa.edu.cn
• 作者简介:邱净博,女,硕士研究生。主要研究方向:协同跟踪;李清东,男,博士,讲师。主要研究方向:导航制导与控制。
• 基金资助:
中航工业创新基金（cxy2012BH01）

### Comparison of uncertainty in state equation based on probabilistic approach and interval analysis method

QIU Jingbo, REN Zhang, LI Qingdong, DONG Xiwang

1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
• Received:2016-01-06 Online:2017-01-20 Published:2016-05-23
• Supported by:
Innovation Found of Aviation Industry Corporation of China (cxy2012BH01)

Abstract: Based on the solution algorithm of state equation in modern control theory, analysis and comparison between interval analysis method and stochastic process are proposed to solve control system with uncertain but bounded parameters. After the definition and influence of uncertainty in engineering practice are known, the uncertain parameters were expressed in the forms of interval and stochastic process. To obtain the response of the system, uncertain variables are divided into the one related to initial condition and the other concerned in system input:zero input response and zero state response. According to extension principle of interval function in interval analysis and Chebyshev's inequality in probability and statistics theory, based on mathematical proof and numerical calculation, the problem of compatibility of using non-probabilistic interval analysis method and probabilistic approach is resolved. The results illustrate that with the uncertain input interval vector which is acquired by probabilistic approach, the system's response interval acquired by non-probabilistic interval analysis method contains the one obtained by probabilistic approach.