| 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)
|
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.
| [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.
|
| [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.
|
Figures(4)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@cqjj8.com
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
