奇异值分解法及其在辨识和控制中的应用

张洪钺

张洪钺. 奇异值分解法及其在辨识和控制中的应用[J]. 信息与控制, 1983, 12(3): 36-41.
引用本文: 张洪钺. 奇异值分解法及其在辨识和控制中的应用[J]. 信息与控制, 1983, 12(3): 36-41.
Zhang Hongyue. The Singular Value Decomposition and its Application in Identification and Control[J]. INFORMATION AND CONTROL, 1983, 12(3): 36-41.
Citation: Zhang Hongyue. The Singular Value Decomposition and its Application in Identification and Control[J]. INFORMATION AND CONTROL, 1983, 12(3): 36-41.

奇异值分解法及其在辨识和控制中的应用

The Singular Value Decomposition and its Application in Identification and Control

  • 摘要: 奇异值分解法是数值计算中的一个重要方法,目前在控制领域中正在得到日益广泛的使用.本文概要说明,在数字计算机上进行运算时,计算结果受机器浮点数系统精度的影响,其程度与计算问题本身是病态或常态,以及所用计算方法是否稳定有关.进而说明奇异值分解法是一种非常有效的数值方法.介绍了奇异值分解定理,奇异值和奇异向量的一些基本性质.最后说明奇异值分解法在系统辨识和控制设计中的若干应用.
    Abstract: Singular value decomposition(SVD)is an important topic in numerical computation.It has gained wide application in control field.And it is illustrated in this paper that the floating point arithmetic of the machine affects the accuracy of the calculation to an extent which largely depends upon the problem itself and the stability of the computing method used.Finally,the SVD theorem and some basic properties of the singular value andsingular vector are introduced.And some of its application in system control and identification are given.
  • [1] K1ema,V.C.and Laub,A.d.,The Singular Value Decomposition:Its Computation and Some Application.IEEE.Trans.,AC-25,No,2,April 1980.
    [2] MacDuffee,C.C.,The Theory of Matrices,Berlin:Springer,1933.
    [3] Autonne,L.,Bull.Soc.Math,France,Vol.30,pp.121-133,1902.
    [4] Ekart,C,and Young,G.,A Principal Axis Transformation for non-Hermitian Matrices. Bull,Amer.Math,Soc.,Yo1.45,pp181-121,1939.
    [5] Paige,C.C.,Properties of Numerical Algorithms Related to Computing Controlability,IEEE,Trans.,AC-26,No.l, Feb.,1981.
    [6] Forsythe,G.E., Malcolm,M.A, and Moler,C.B.,Computer Methods for Mathematical Computation, Englewood Cliffs, NJ:Preatice-Hall,1977.
    [7] Stewart,G.W.,Introduction to Matrix Compotations,New York:Academic,1973,
    [8] Smith,B.T,et al.,Matrix Eigensystem Routines-EISPACK Guide,2nd ed.(Lecture Notes in Compct,Sci.)Vo1.6,New York:Springer-Verlag,1976,
    [9] Garbow.B.S,et al.,Matrix Eigensystem Routines-EISPACK Guide Extension (Lect,Notes in Comput,Sci.),Vo1.51,New York:Springer-Verlag,1977,
    [10] Dongarra,J.J.et al.,LINPACK User's Guide, Philadelphia, PA:SIAM,1979.
    [11] Cruz, Jr.,J.B.et al.,A Relationship between Sensitivity and Stability of Multicariable Feedback Systems,IEEE Trans.AC-26,No.l,Feb.,1981.
    [12] Lehtomaki. N.A, Sandell,Jr.,N.R, and Athans, M Robustness Results in Linear-Quadratic Caussian based Multivariable Control Designs, IEEE Trans,AC-26,No.1,Feb.,1981.
    [13] Lawson,C,L,and Hanson, R,3.,Solving Least Squares Problems. Englewood Cliffs. NJ:Prentice-Hall,1974.
    [14] Zhang,H.Y,(张洪钺),Shieh,L.S.,Yates.R,E, Identification and Model Reduction of Multivariable Continuous Systems via a Block-pulse Functions Scheme,Applied Mathematical Modelling,1982,Yo1.6,Oct.,pp,369-372.
    [15] Zeiger,H.P.and McEwen,A,J.,Approximate Linear Realizations of Given Dimension via Ho's A1gorithm,IEEE Trans.,AC-l9,No.2,April,1974,
    [16] Doyle,l.C, and Stein,G.,Multivariable Feedback Design:Concepts for a Classical/Modern Synthesis,IEEE Trans.,AC-26.No.l,Feb.,1981.
    [17] Postlethwaite,L.,Edmunds,l.M, snd Macfarlane,A.G.J.,Principal Gains and Principal Plisses is the Analysis of linear Multivariable Feedback,Systems,IEEE Trans.AC-26, No.1,Feb.,1981,
    [18] Moore,B.C.,Principal Component Analysis in Linear System:Controllability,Observability.and Model Reduction,IEEE Trans.,AC-26,No.l,Feb.,1981,
    [19] Andrews,H.C.and Patterson,C,L.,Outer Product Expansions and Their Uses in Digital Image Processing,American Math.,Monthly,Vo1.82,pp,l-12,1975,
计量
  • 文章访问数:  561
  • HTML全文浏览量:  0
  • PDF下载量:  195
  • 被引次数: 0
出版历程
  • 收稿日期:  1982-01-02
  • 发布日期:  1983-06-19

目录

    /

    返回文章
    返回
    x