In this paper we develop a method for identifying SISO Wiener-type nonlinear systems, that is, systems consisting of a linear dynamic system followed by a static nonlinearity. Unlike previous techniques developed for Wiener system identification, our approach allows the identification of systems with nonlinearities that are known but not necessarily invertible, continuous, differentiable, or analytic.

1.
Ljung, Lennart, 1999, System Identification: Theory for the User, Prentice Hall Information and System Sciences Series. Prentice Hall, 2nd edition, Jan.
2.
Juang, Jer-Nan, 1999, Applied System Identification, Prentice Hall.
3.
Van Overschee, Peter and De Moor, Bart, 1996, Subspace Identification for Linear Systems: Theory, Implementation, Applications, Kluwer.
4.
Soderstrom, Torsten, and Stoica, Petre, 1989, System Identification, Prentice Hall.
5.
Ahmed-Zaid, F., Ioannou, P. A., and Polycarpou, M. M., 1993, “Identification and control of aircraft dynamics using radial basis function networks,” Second IEEE Conference on Control Applications, Vancouver, BC, Sept., pp. 567–572.
6.
Juditsky
et al.
,
1995
, “
Nonlinear black-box models in system identification: Mathematical foundations
,”
Automatica
,
31
, No.
12
, pp.
1725
1750
.
7.
Songwu
,
Lu
, and
Tamer
,
Bas¸ar
,
1998
, “
Robust nonlinear system identification using neural-network models
,”
IEEE Trans. Neural Netw.
,
9
, No.
3
, May, pp.
407
429
.
8.
Chen
,
S.
,
Billings
,
S. A.
, and
Grant
,
P. M.
,
1990
, “
Non-linear system identification using neural networks
,”
Int. J. Control
,
51
, No.
6
, pp.
1191
1214
.
9.
Chen
,
S.
,
Billings
,
S. A.
,
Cowan
,
C. F. N.
, and
Grant
,
P. M.
,
1990
, “
Non-linear systems identification using radial basis functions
,”
Int. J. Syst. Sci.
,
21
, No.
12
, pp.
2513
2539
.
10.
Narendra
,
Kumpati S.
, and
Parthasarathy
,
Kannan
,
1990
, “
Identification and control of dynamical systems using neural networks
,”
IEEE Trans. Neural Netw.
,
1
, No.
1
, pp.
4
27
.
11.
Chen
,
S.
, and
Billings
,
S. A.
,
1992
, “
Neural networks for nonlinear dynamic system modelling and identification
,”
Int. J. Control
,
56
, No.
2
, pp.
319
346
.
12.
Brillinger
,
D. R.
,
1970
, “
The identification of polynomial systems by means of higher order spectra
,”
J. Sound Vib.
,
12
, No.
3
, pp.
301
313
.
13.
Westwick
,
D. T.
, and
Kearney
,
R. E.
,
1992
, “
A new algorithm for the identification of multiple input Wiener systems
,”
Biol. Cybern.
,
68
, pp.
75
85
.
14.
Wigren
,
Torbjo¨rn
,
1994
, “
Convergence analysis of recursive identification algorithms based on the Wiener model
,”
IEEE Trans. Autom. Control
,
39
, No.
11
, pp.
2191
2206
.
15.
Greblicki
,
Włodzimierz
,
1997
, “
Nonparametric approach to Wiener system identification
,”
IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
,
44
, No.
6
, pp.
538
545
.
16.
Grazyna A. Pajunen, 1985, “Recursive identification of Wiener type nonlinear systems,” Proceedings of the 1985 American Control Conference, Vol. 3, Boston, MA, June, pp. 1365–1370.
17.
Hasiewicz
,
Z.
,
1987
, “
Identification of a linear system observed through zero-memory non-linearity
,”
Int. J. Syst. Sci.
,
18
, No.
9
, pp.
1595
1607
.
18.
Bai
,
Er-Wei
,
1998
, “
An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems
,”
Automatica
,
34
, No.
3
, pp.
333
338
.
19.
Greblicki
,
Włodzimierz
,
1994
, “
Nonparametric identification of Wiener systems by orthogonal series
,”
IEEE Trans. Autom. Control
,
39
, No.
10
, pp.
2077
2086
.
20.
Chen
,
C. H.
, and
Fassois
,
S. D.
,
1992
, “
Maximum likelihood identification of stochastic Wiener-Hammerstein-type non-linear systems
,”
Mech. Syst. Signal Process.
,
6
, No.
2
, pp.
135
153
.
21.
Greblicki
,
Włodzimierz
,
1992
, “
Nonparametric identification of Wiener systems
,”
IEEE Trans. Inf. Theory
,
38
, No.
5
, pp.
1487
1493
.
22.
Lovera
,
Marco
,
Gustafsson
,
Tony
, and
Verhaegen
,
Michel
,
2000
, “
Recursive subspace identification of linear and non-linear Wiener state-space models
,”
Automatica
,
36
, pp.
1639
1650
.
23.
Westwick
,
David
, and
Verhaegen
,
Michel
,
1996
, “
Identifying MIMO Wiener systems using subspace model identification methods
,”
Signal Process.
,
52
, pp.
235
258
.
24.
Emara-Shabaik
,
Hosam E.
,
Moustafa
,
Kamal A. F.
, and
Talaq
,
Jaleel H. S.
,
1995
, “
On identification of parallel block-cascade nonlinear models
,”
Int. J. Syst. Sci.
,
26
, No.
7
, pp.
1429
1438
.
25.
Sjo¨berg
et al.
,
1995
, “
Nonlinear black-box modeling in system identification: A unified overview
,”
Automatica
,
31
, No.
12
, pp.
1691
1724
.
26.
Chen, C.-H. and Fassois S. D., 1997, “On the estimation of stochastic Wiener-Hammerstein-type systems with non-smooth non-linearity,” Proceedings of the 1997 American Control Conference, Albuquerque, NM.
27.
Hunter
,
I. W.
, and
Korenberg
,
M. J.
,
1986
, “
The identification of nonlinear biological systems: Wiener and Hammerstein cascade models
,”
Biol. Cybern.
,
55
, pp.
135
144
.
28.
Korenberg
,
M. J.
, and
Hunter
,
I. W.
,
1986
, “
The identification of nonlinear biological systems: LNL cascade models
,”
Biol. Cybern.
,
55
, pp.
125
134
.
29.
Wang, LeYi, Kolmanovsky, Ilya, and Sun, Jing, 2000, “On-line identification and adaption of lnt models for improved emission control in lean burn automotive engines,” Proceedings of the American Control Conference, Chicago IL, June, pp. 1006–1010.
30.
Bayard, David S. and Eslami Mansour, 1984, “Parameter identification of linear systems using nonlinear noninvertible measurements,” Proceedings of the 23rd Conference on Decision and Control, IEEE, Dec., pp. 348–352.
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