This paper considers identification problems for Wiener systems with saturation and dead-zone nonlinearities. The basic idea is to obtain the identification model of such a nonlinear system using a switching function, and to propose a gradient-based iterative identification algorithm using the iterative technique. An example is provided to show the effectiveness of the proposed algorithm.
BaiEW (1998) An optimal two-stage identification algorithm for Hammerstein–Wiener nonlinear systems. Automatica34(3): 333–338.
2.
BaiEW (2002) Identification of linear systems with hard input nonlinearities of known structure. Automatica38(5): 853–860.
3.
ChenJLvLXDingRF (2012a) Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity. Applied Mathematics Letters. DOI:10.1016/j.bbr.2011.03.031.
4.
ChenJWangXPDingRF (2012b) Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities. Applied Mathematical Modelling36(1): 238–243.
5.
ChenJZhangYDingRF (2010) Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Mathematical and Computer Modelling52(9–10): 1428–1434.
6.
ChenJZhangYDingF (2011a) Gradient based iterative algorithm for Wiener systems with piece-wise nonlinearities using analytic parameterization methods. Computers and Applied Chemistry28(7): 855–857.
7.
ChenJZhangYDingF (2011b) Least squares based iterative parameter estimation for output nonlinear systems with piece-wise nonlinearities. Proceedings of the 30th Chinese Control Conference. Yantan, China, 1438–1441. 22–24 July 2011.
8.
DingF (2010) Several multi-innovation identification methods. Digital Signal Processing20(4): 1027–1039.
9.
DingF (2012) Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Applied Mathematical Modelling. DOI:10.1016/j.apm.2012.04.039.
10.
DingFChenT (2005a) Identification of Hammerstein nonlinear ARMAX systems. Automatica41(9): 1479–1489.
11.
DingFChenT (2005b) Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Transactions on Circuits and Systems–I: Regular Papers52(6): 1179–1187.
12.
DingFChenT (2005c) Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control50(3): 397–402.
DingFChenT (2007) Performance analysis of multi-innovation gradient type identification methods. Automatica43(1): 1–14.
15.
DingFDingJ (2010) Least squares parameter estimation with irregularly missing data. International Journal of Adaptive Control and Signal Processing24(7): 540–553.
16.
DingJDingF (2011) Bias compensation based parameter estimation for output error moving average systems. International Journal of Adaptive Control and Signal Processing25(12): 1100–1111.
17.
DingJDingFLiuXP (2011a) Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Transactions on Automatic Control56(11): 2677–2683.
18.
DingJHanLLChenXM (2010a) Time series AR modeling with missing observations based on the polynomial transformation. Mathematical and Computer Modelling51(5–6): 527–536.
19.
DingFLiuYJBaoB (2012) Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering226(1): 43–55.
20.
DingFLiuXPLiuG (2009a) Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Processing89(10): 1883–1890.
21.
DingFLiuXPLiuG (2010b) Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digital Signal Processing20(3): 664–677.
22.
DingFLiuGLiuXP (2011b) Parameter estimation with scarce measurements. Automatica47(8): 1646–1655.
23.
DingFLiuXPLiuG (2011c) Identification methods for Hammerstein nonlinear systems. Digital Signal Processing21(2): 215–238.
24.
DingFLiuXPYangHZ (2008) Parameter identification and intersample output estimation for dual-rate systems. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans38(4): 966–975.
25.
DingFQiuLChenT (2009b) Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica45(2): 324–332.
26.
DingFShiYChenT (2007) Auxiliary model-based least-squares identification methods for Hammerstein output-error systems. Systems & Control Letters56(5): 373–380.
27.
HanLLDingF (2009) Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digital Signal Processing19(4): 545–554.
28.
LiJHDingF (2011) Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique. Computers and Mathematics with Applications62(11): 4170–4177.
29.
LiJHDingFYangGW (2012) Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Mathematical and Computer Modelling55(3–4): 442–450.
30.
LiuYJShengJDingRF (2010a) Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Computers and Mathematics with Applications59(8): 2615–2627.
31.
LiuYJWangDQDingF (2010b) Least-squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data. Digital Signal Processing20(5): 1458–1467.
32.
LiuYJXiaoYSZhaoXL (2009a) Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Applied Mathematics and Computation215(4): 1477–1483.
33.
LiuYJXieLDingF (2009b) An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems. Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering223(4): 445–454.
34.
ShiYChenT (2003) Optimal design of multi-channel transmultiplexers with stopband energy and passband magnitude constraints. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing50(9): 659–662.
35.
ShiYDingFChenT (2006) Multirate crosstalk identification in xDSL systems. IEEE Transactions on Communications54(10): 1878–1886.
36.
ShiYFangH (2010) Kalman filter based identification for systems with randomly missing measurements in a network environment. International Journal of Control33(3): 538–551.
37.
ShiYFangHYanM (2009) Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs. International Journal of Robust and Nonlinear Control, Special Issue on Control with Limited Information (Part II)19(18): 1976–1992.
38.
VörösJ (2001) Parameter identification of Wiener systems with discontinuous nonlinearities. Systems and Control Letters44(5): 363–372.
39.
VörösJ (2002) Modeling and parameter identification of systems with multisegment piecewise-linear characteristics. IEEE Transactions on Automatic control47(1): 184–188.
40.
VörösJ (2007) Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Systems and Control Letters56(2): 99–105.
41.
VörösJ (2010) Modeling and identification of systems with backlash. Automatica46(2): 369–374.
42.
WangDQDingF (2008) Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems. Computers and Mathematics with Applications56(12): 3157–3164.
43.
WangDQDingF (2010) Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digital Signal Processing20(3): 750–762.
44.
WangDQDingF (2011) Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Processing91(5): 1182–1189.
45.
XiaoYSYueN (2011) Parameter estimation for nonlinear dynamical adjustment models. Mathematical and Computer Modelling54(5–6): 1561–1568.
46.
XieLLiuYJYangHZ (2010) Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theory and Applications4(5): 784–794.
47.
XieLYangHZ (2011) Gradient based iterative identification for non-uniform sampling output error systems. Journal of Vibration and Control17(3): 471–478.
48.
YuBFangHLinY (2010) Identification of Hammerstein output-error systems with two-segment nonlinearities: algorithm and applications. Control and Intelligent Systems38(4): 194–201.
49.
ZhangJBDingFShiY (2009) Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Systems and Control Letters58(1): 69–75.