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基于随机与区间分析的状态方程不确定性比较

邱净博 任章 李清东 董希旺

邱净博, 任章, 李清东, 等 . 基于随机与区间分析的状态方程不确定性比较[J]. 北京航空航天大学学报, 2017, 43(1): 151-158. doi: 10.13700/j.bh.1001-5965.2016.0021
引用本文: 邱净博, 任章, 李清东, 等 . 基于随机与区间分析的状态方程不确定性比较[J]. 北京航空航天大学学报, 2017, 43(1): 151-158. doi: 10.13700/j.bh.1001-5965.2016.0021
QIU Jingbo, REN Zhang, LI Qingdong, et al. Comparison of uncertainty in state equation based on probabilistic approach and interval analysis method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(1): 151-158. doi: 10.13700/j.bh.1001-5965.2016.0021(in Chinese)
Citation: QIU Jingbo, REN Zhang, LI Qingdong, et al. Comparison of uncertainty in state equation based on probabilistic approach and interval analysis method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(1): 151-158. doi: 10.13700/j.bh.1001-5965.2016.0021(in Chinese)

基于随机与区间分析的状态方程不确定性比较

doi: 10.13700/j.bh.1001-5965.2016.0021
基金项目: 

中航工业创新基金 cxy2012BH01

详细信息
    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

    通讯作者:

    E-mail:liqingdong@buaa.edu.cn

  • 中图分类号: TP13

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

Funds: 

Innovation Found of Aviation Industry Corporation of China cxy2012BH01

More Information
  • 摘要:

    基于现代控制理论中状态方程的求解算法,对具有参数不确定性的控制系统采用非概率区间分析方法与随机控制理论进行研究。首先明确实际工程应用中不确定性的概念和影响,分别建立了区间值和随机过程2种描述方法,求解系统的响应区间,并分为与初始条件和输入相关的零输入和零状态两部分不确定量。根据区间数学中的区间函数扩张原理和概率统计理论中的切比雪夫不等式,从数学证明和数值计算2个方面,分别用非概率区间分析和概率统计方法求解不确定系统的响应,并对二者进行比较,分析其相容性。结果表明,在由概率统计信息得到不确定性变量的区间向量为系统输入的情况下,非概率区间分析方法得到的响应区间包含由随机控制理论得到的响应区间。

     

  • 图 1  无扰动量的第一自由度位移响应曲线

    Figure 1.  First degree of freedom of displacement responsecurves without uncertainty

    图 2  随机过程的系统响应区间

    Figure 2.  System response interval of state equation byprobabilistic approach

    图 3  区间分析的系统响应区间

    Figure 3.  System response interval of state equation byinterval analysis method

    图 4  随机过程和区间分析的系统响应区间比较

    Figure 4.  Comparison of system response intervals of state equation obtained by probabilistic approachand interval analysis method

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出版历程
  • 收稿日期:  2016-01-06
  • 录用日期:  2016-04-29
  • 网络出版日期:  2017-01-20

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