System identification based on Hammerstein model. (English) Zbl 1134.93411

The Hammerstein system identification is considered. A scheme yielding the estimates of the linear dynamics parameters and a freely selected number of plot points \((x,F(x))\) of a nonlinear characteristic \(F(.)\) is proposed. It is assumed that the nonlinearity is bounded and vanishes at the origin. The identification routine is parametric and based on the idea of polynomial interpolation of the plot points \(\{(x,F(x)\}\), recursive least squares/prediction error method for estimation of system parameters under, respectively, bounded and ARMA-type noise, and a singular value decomposition for separation of the obtained aggregated identification outcomes. For the bounded noise case, the estimation errror upper bound is established, and for a noise-free case convergence of the resulting estimates is concluded assuming a particular, impulse-type, system input. Simulation illustrative examples support the theory.


93E12 Identification in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
93B30 System identification
93C80 Frequency-response methods in control theory
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[1] Bai EW, Automatica 34 pp pp. 333–338– (1998)
[2] Billings SA, Int. J. Syst. Sci. 10 pp pp. 567–578– (1979)
[3] Giri F, Automatica 37 pp pp. 749–756– (2001)
[4] DOI: 10.1016/S0005-1098(01)00222-9 · Zbl 1021.93012 · doi:10.1016/S0005-1098(01)00222-9
[5] Giri F, Automatica 27 pp pp. 153–160– (1990)
[6] Gomez JC Bayens E ”Identification of multivariable Hammerstein systems using rotational orthonormal bases” IEEE Conference on Decision and Control Sydney Australia 2000
[7] Greblicki W, Int. J. Systems Sciences 20 pp pp. 2355–2367– (1989) · Zbl 0688.93062
[8] DOI: 10.1016/0165-1684(91)90029-I · Zbl 0725.93028 · doi:10.1016/0165-1684(91)90029-I
[9] Greblicki W, Control-theory and Advanced Technology 10 pp pp. 771–791– (1994)
[10] Krzyzak A, Int. J. Systems Sciences 20 pp pp. 1729–1744– (1989)
[11] Kung FC, Int. J. Control 43 pp pp. 139–147– (1986)
[12] Lang ZQ, Automatica 29 pp pp. 767–771– (1993)
[13] Lang ZQ, IEEE-TAC 42 pp pp. 1435–1441– (1997)
[14] Ljung L, System Identification-theory for the User (1999)
[15] Pawlak M, IEEE-TAC 36 pp pp. 736–767– (1991)
[16] Stoica P, Int. J. control 35 pp pp. 459–476– (1982)
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