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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

  • [1] DE OLIVEIRA L P R,VAROTO P S,SAS P,et al.A state-space modeling approach for active structural acoustic control[J].Shock and Vibration,2009,16(6):607-621. doi: 10.1155/2009/797125
    [2] 尤昌德.现代控制理论基础[M].北京:电子工业出版社,1996:18-25.

    YOU C D.Basis of modern control theory[M].Beijing:Electronics Industry Press,1996:18-25(in Chinese).
    [3] TAGHIPOUR R,PEREZ T,MOAN T.Hybrid frequency-time domain models for dynamic response analysis of marine structures[J].Ocean Engineering,2008,35(7):685-705 doi: 10.1016/j.oceaneng.2007.11.002
    [4] JOHANSSON A.A sufficient condition for invalidation of linear state-space systems with uncertain time-varying parameters[J].IEEE Transactions on Automatic Control,2009,54(12):2915-2920. doi: 10.1109/TAC.2009.2033860
    [5] 华东师范大学数学系控制理论教研室.现代控制理论引论[M].上海:华东师范大学,1983:67-85.

    Mathematics Department of East China Normal University.Introduction of modern control theory[M].Shanghai:East China Normal University,1983:67-85(in Chinese).
    [6] WILLIAM L O.Challengeproblems:Uncertainty in system response given uncertain parameters[J].Reliability Engineering and System Safety,2004,85(7):11-19.
    [7] ELISHAKOFF I.Three versions of the finite element method based on concepts of either stochasticity,fuzziness or anti-optimization[J].Applied Mechanics Review,1998,51(3):209-218. doi: 10.1115/1.3098998
    [8] 方洋旺.随机系统最优控制[M].北京:清华大学出版社,2005:54-62.

    FANG Y W.Optimalcontrol of stochastic control[M].Beijing:Tsinghua University Press,2005:54-62(in Chinese).
    [9] WIENR N.Extrapolation,interpolation,and smoothing of stationary time series:OSRD70,report to the Services 19,research project DIC-6037[R].Cambridge:MIT,1942.
    [10] KALMAN R E.A new approach to linear filtering and prediction problems[J].Journal of Basic Engineering,1960,82(Series D):35-45. http://cn.bing.com/academic/profile?id=e02195a257d103d9b22123ac1731e809&encoded=0&v=paper_preview&mkt=zh-cn
    [11] KALMAN R E,BUCY R S.New result in linear filtering and prediction theory[J].Journal of Basic Engineering,1961,83:95-108. doi: 10.1115/1.3658902
    [12] 陈相志.区间多项式稳定性的研究[D].天津:天津大学,2005:44-57.

    CHEN X Z.Study of stability of interval polynomial[D].Tianjin:Tianjin University,2005:44-57(in Chinese).
    [13] CHEN G R,WANG J R,SHIEN L S.Interval Kalman filtering[J].IEEE Transactions on Aerospace and Electronic Systems,1997,33(1):250-258. doi: 10.1109/7.570759
    [14] 吴杰,陈塑寰.区间参数结构的动力响应优化[J].固体力学学报,2004,25(2):186-190. http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200402011.htm

    WU J,CHEN S H.Optimation of the dynamic response of an intervalparameter structure[J].Solid Mechanics,2004,25(2):186-190(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200402011.htm
    [15] 孙先仿.集员辨识——算法、收敛性和鲁棒性[D].北京:中国科学院,1994:47-48.

    SUN X F.Setmembership identification-algorithm,stability and robustness[D].Beijing:Chinese Academy of Sciences,1994:47-48(in Chinese).
    [16] ANDERSON B D O,MOORE J B.Optimalfiltering[M].Englewood Cliffs,NJ:Prentice-Hall,1999:77-89.
    [17] 曾开春,向锦武.高超声速飞行器飞行动力学特性不确定分析[J].航空学报,2013,34(4):79-88. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201304010.htm

    ZENG K C,XIANG J W.Uncertainty analysis of flight dynamic characteristics for hypersonic vehicles[J].Acta Aeronautica et Astronautica Sinica,2013,34(4):79-88. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201304010.htm
    [18] QIU Z P,WANG X J.Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach[J].International Journal of Solids and Structures,2003,40(8):5423-5439. http://cn.bing.com/academic/profile?id=214a2905b232409b7fdd8ee50e8965e1&encoded=0&v=paper_preview&mkt=zh-cn
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出版历程
  • 收稿日期:  2016-01-06
  • 录用日期:  2016-04-29
  • 刊出日期:  2017-01-20

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