Articles

RECURSIVE SYSTEM IDENTIFICATION

  • Han-Fu Chen
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  • Key Laboratory of Systems and Control, Institute of Systems Science, AMSS Chinese Academy of Sciences, Beijing 100190, China

Received date: 2008-12-10

  Online published: 2009-05-20

Supported by

The work is supported by NSFC (60221301 and 60874001) and by a grant from the National Laboratory of Space Intelligent Control

Abstract

Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive. This paper demonstrates the recent progress in recursive system identification. The recursive identifi-cation algorithms are presented not only for linear systems (multivariate ARMAX systems) but also for nonlinear systems such as the Hammerstein and Wiener systems, and the non-
linear ARX systems. The estimates generated by the algorithms are online updated and converge a.s. to the true values as time tends to infinity.

Cite this article

Han-Fu Chen . RECURSIVE SYSTEM IDENTIFICATION[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 650 -672 . DOI: 10.1016/S0252-9602(09)60062-X

References


[1] Bai E W, Li D. Convergence of the iterative Hammerstein system identification algorithm. IEEE Trans
Automat Contr, 2004, 49(11): 1929–1940


[2] Bai E W, Liu Y. Recursive direct weight optimization in nonlinear system identification: a minimal
probability approach. IEEE Trans Automat Contr, 2007, 52(7): 1218–1231


[3] Bai E W, Tempo R, Liu Y. Identification of IIR nonlinear systems without prior structural information.
IEEE Trans Automat Contr, 2007, 52(3): 442–453


[4] Benveniste A, M´etivier M, Priouret P. Adaptive Algorithms and Stochastic Approximations. New York:
Springer-Verlag, 1990


[5] Box G E P, Jenkins G. Time Series Analysis, Forecasting and Control. San-Francisco: Holden-Day, 1970


[6] Brockwell P J, Davis R A. Time Series, Theory and Methods. Second Edition. Heidelberg: Springer-Verlag, 2001


[7] Caines P E. Linear Stochastic Systems. New York: Wiley, 1988


[8] Chen H F. Stochastic Approximation and Its Applications. Dordrecht: Kluwer, 2002


[9] Chen H F. Pathwise convergence of recursive identification algorithms for Hammerstein systems. IEEE
Trans Automat Contr, 2004, 49(10): 1641–1649


[10] Chen H F. Strong consistency of recursive identification for Hammerstein systems with piecewise-linear
memoryless block. IEEE Trans Autom Control, 2005, 50(10): 1612–1617


[11] Chen H F. Recursive identification for Wiener model with discontinuous piece-wise linear function. IEEE
Trans Automat Contr, 2006, 51(3): 390–400


[12] Chen H F. New approach to recursive identification for ARMAX systems. Submitted for publication


[13] Chen H F, Guo L. Identification and Stochastic Adaptive Control. Boston: Birkhäuser, 1991


[14] Chen H F, Zhu Y M. Stochastic approximation procedures with randomly varying truncations. Scientia
Sinica (Series A), 1986, 29(9): 914–926


[15] Claerbout J F. Spectral factorization of multiple time series. Biometrica, 1966, 53(1): 264–267


[16] Fan J Q, Yao Q. Nonlinear Time Series: Nonparametric and Parametric Approach. New York: Springer-
Verlag, 2003


[17] Georgiev A A. Nonparametric system identification by kernel methods. IEEE Trans Automat Contr, 1984,
29(4): 356–358


[18] Greblicki W. Stochastic approximation in nonparametric identification of Hammerstein systems. IEEE
Trans Automat Contr, 2002, 47(11): 1800–1810


[19] Guo L, Huang D. Least squares identification for ARMAX models without the positive real condition.
IEEE Trans Autom Control, 1989, 34: 1094–1098


[20] Hannan E J. The identification of vector mixed autoregressive-moving average systems. Biometrica, 1969,
56: 223–225


[21] Hannan E J. The estimation of ARMA models. The Annals of Statistics, 1975, 3(4): 975–981


[22] Hannan E J, Diestler M. The Statistical Theory of Linear Systems. New York: Wiley, 1988


[23] Hu X L, Chen H F. Strong consistency of recursive identification for Wiener systems. Automatica, 2005,
41(11): 1905–1916


[24] Hu X L, Chen H F. Identification for Wiener Systems with RTF Subsystems. European Journal of Control,
2006, 6: 581–594


[25] Huang Y Q, Chen H F, Fang H T. Identification of Wiener Systems with Nonlinearity Being Piecewiselinear
Function. Science in China Series F: Information Science, 2008, 51(1): 1–12


[26] Kushner H J, Yin G G. Stochastic Approximation and Recursive Algorithms and Applications. Second
Edition. New York: Springer, 2003


[27] Lai T L, Ying Z. Recursive selections of estimating algorithms and adaptive spectral factorization. IEEE
Trans Autom Control, 1992, 37(2): 240–243


[28] Lai T L, Wei C Z. Least squares estimates in stochastic regression models with application to identification
and control of dynamic systems. Ann Stat, 1983, 10(1): 154–166


[29] Ljung L. System Identification: Theory for Users. 2nd edition. Upper Saddle River, NJ: Prentice Hall,
1999


[30] Ljung L. Perspectives on system identification//Chung M J, Misra P, eds. Plenary Papers, Milestone
Reports & Selected Survey Papers, 17th IFAC World Congress. July 6-11, 2008, Seoul: 47–59


[31] Ljung L, S¨oderstr¨om T. Theory and Practice of Recursive Identification. Cambridge, MA: MIT Press,
1983


[32] Markovsky I, Willems J C, De Moore B. The model structure of ARMAX systems, Proceedings of the 41st
IEEE Conference on Decision and Control. San Diego, USA, 2006. 811–816


[33] Robbins H, Monro S. A stochastic approximation method. Ann Math Statist, 1951, 22: 400–407


[34] Song Q J, Chen H F. Identification of errors-in-variables systems with ARMA observation noises. Systems
and Control Letters, 2008, 57(5): 420–424


[35] Stoica P. Generalized Yule-Walker equations and testing the order of multivariate time series. Int J Control,
1983, 37(5): 1159–1166


[36] Stoica P, McKelvey T, Mari J. MA estimation in polynomial time. IEEE Trans Signal Processing, 2000,
48(7): 1999–2012

[37] V¨orös J. Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities.
Systems and Control Letters, 2007, 56: 99–105


[38] Zhao W X, Chen H F. Recursive identification for Hammerstein system with ARX subsystem. IEEE Trans
Autom Control, 2006, 51(12): 1966–1974


[39] Zhao W X, Chen H F. Recursive identification for nonlinear ARX systems. submitted for publication

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