Iterative identification algorithm for Wiener nonlinear systems using the Newton method

Applied Mathematical Modelling

Volumn 37, Issue 9, 2013, Pages 6584-6591

  Liu, Manman ^a   Xiao, Yongsong ^a   Ding, Ruifeng ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Iterative identification; Newton iteration; Nonlinear systems; Parameter estimation; Wiener systems

Indexed keywords

COLORED NOISE; ITERATIVE IDENTIFICATION; ITERATIVE PARAMETER ESTIMATION; NEWTON ITERATIONS; WIENER SYSTEMS;

NEWTON-RAPHSON METHOD; NONLINEAR SYSTEMS; PARAMETER ESTIMATION;

ALGORITHMS;

EID: 84875375057     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.01.025     Document Type: Article

References (59)

1. Chen J., Wang X.P., Ding R.F. Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities. Appl. Math. Model. 2012, 36(1):238-243.
2. Ding F., Shi Y., Chen T. Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dyn. 2006, 45(1-2):31-43.
3. Ding F., Chen T., Iwai Z. Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM J. Control Optim. 2007, 45(6):2257-2276.
4. Zhang J.B., Ding F., Shi Y. Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Control Lett. 2009, 58(1):69-75.
5. Yu B., Fang H., et al. Identification of Hammerstein output-error systems with two-segment nonlinearities: algorithm and applications. Control Intell. Syst. 2010, 38(4):194-201.
6. Ding F., Shi Y., Chen T. Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 2007, 56(5):373-380.
7. Wang D.Q., Ding F. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 2011, 91(5):1182-1189.
8. Wang D.Q., Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Comput. Math. Appl. 2008, 56(12):3157-3164.
9. Dehghan M., Hajarian M. An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Appl. Math. Model. 2010, 34(3):639-654.
10. Dehghan M., Hajarian M. Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 2011, 35(7):3285-3300.
11. Ding F., Liu X.P., Ding J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl. Math. Comput. 2008, 197(1):41-50.
12. Xie L., Ding J., et al. Gradient based iterative solutions for general linear matrix equations. Comput. Math. Appl. 2009, 58(7):1441-1448.
13. Ding J., Liu Y.J., et al. Iterative solutions to matrix equations of form AiXBi=Fi. Comput. Math. Appl. 2010, 59(11):3500-3507.
14. Ding F., Shi Y., Chen T. Performance analysis of estimation algorithms of non-stationary ARMA processes. IEEE Trans. Signal Process. 2006, 54(3):1041-1053.
15. Ding F., Yang H.Z., Liu F. Performance analysis of stochastic gradient algorithms under weak conditions,. Sci. China Ser. F-Inf. Sci. 2008, 51(9):1269-1280.
16. Ding F., Liu G., Liu X.P. Parameter estimation with scarce measurements. Automatica 2011, 47(8):1646-1655.
17. Ding F., Liu Y.J., Bao B. Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng. Part I 2012, 226(1):43-55.
18. Shi Y., Fang H. Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 2010, 83(3):538-551.
19. Shi Y., Fang H., Yan M. Kalman filter-based adaptive control for networked systems with unknown parameters and randomly missing outputs. Int. J. Robust Nonlinear Control 2009, 19(18):1976-1992.
20. Ding F., Chen T. Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. - I: Regul. Pap. 2005, 52(6):1179-1187.
21. Ding F., Qiu L., Chen T. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 2009, 45(2):324-332.
22. Bao B., Xu Y.Q., et al. Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modeling with finite measurement data. Math. Comput. Model. 2011, 53(9-10):1664-1669.
23. Ding F., Liu X.P., Liu G. Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 2010, 20(3):664-677.
24. Ding F., Chen T. Identification of Hammerstein nonlinear ARMAX systems. Automatica 2005, 41(9):1479-1489.
25. Han L.L., Ding F. Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process. 2009, 19(4):545-554.
26. Han L.L., Ding F. Identification for multirate multi-input systems using the multi-innovation identification theory. Comput. Math. Appl. 2009, 57(9):1438-1449.
27. Han L.L., Sheng J., et al. Auxiliary models based recursive least squares identification for multirate multi-input systems. Math. Comput. Model. 2009, 50(7-8):1100-1106.
28. Han L.L., Ding F. Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation. J. Syst. Eng. Electron. 2010, 21(6):1079-1083.
29. Han L.L., Wu F.X., et al. Two recursive least squares parameter estimation algorithms for multirate multiple-input systems by using the auxiliary model. Math. Comput. Simul. 2012, 82(5):777-789.
30. Dehghan M., Hajarian M. Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations. Appl. Math. Lett. 2011, 24(4):444-449.
31. Dehghan M., Hajarian M. A lower bound for the product of eigenvalues of solutions to matrix equations. Appl. Math. Lett. 2009, 22(12):1786-1788.
32. Ding F., Liu X.P., Liu G. Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 2011, 21(2):215-238.
33. Xiong W.L., Ma J.X., Ding R. An iterative numerical algorithm for modeling a class of Wiener nonlinear systems. Appl. Math. Lett. 2013, 26(4):487-493.
34. Liu X.G., Lu J. Least squares based iterative identification for a class of multirate systems. Automatica 2010, 46(3):549-554.
35. Xiao Y.S., Zhang Y., et al. The residual based interactive least squares algorithms and simulation studies. Comput. Math. Appl. 2009, 58(6):1190-1197.
36. Ding J., Ding F., et al. Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 2011, 56(11):2677-2683.
37. Ding J., Ding F. Bias compensation based parameter estimation for output error moving average systems. Int. J. Adapt. Control Signal Process. 2011, 25(12):1100-1111.
38. Li J.H., Ding R.F., Yang Y. Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 2012, 26(6):2739-2750.
39. Ding F., Chen T. Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data. IEEE Trans. Circuits Syst. - I: Regul. Pap. 2005, 52(3):555-566.
40. Ding F., Liu X.P., Yang H.Z. Parameter identification and intersample output estimation for dual-rate systems. IEEE Trans. Syst. Man Cybern. Part A: Syst. Humans 2008, 38(4):966-975.
41. Ding F., Gu Y. Performance analysis of the auxiliary model based least squares identification algorithm for one-step state delay systems. Int. J. Comput. Math. 2012, 89(15):2019-2028.
42. Wang D.Q., Ding F. Hierarchical least squares estimation algorithm for Hammerstein-Wiener systems. IEEE Signal Process. Lett. 2012, 19(12):825-828.
43. Liu Y.J., Xie L., et al. An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems. Proc. Inst. Mech. Eng. Part I 2009, 223(4):445-454.
44. Liu Y.J., Yu L., et al. Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 2010, 29(4):649-667.
45. Yin H.H., Zhu Z.F., et al. Model order determination using the Hankel matrix of impulse responses. Appl. Math. Lett. 2011, 24(5):797-802.
46. Ding F., Liu X.P., Liu G. Multi-innovation least squares identification for linear and pseudo-linear regression models. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 2010, 40(3):767-778.
47. Ding F. Several multi-innovation identification methods. Digit. Signal Process. 2010, 20(4):1027-1039.
48. Xie L., Liu Y.J., et al. Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theor. Appl. 2010, 4(5):784-794.
49. Ding F., Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 2007, 43(1):1-14.
50. Ding F., Liu X.P., Liu G. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 2009, 89(10):1883-1890.
51. Wang D.Q., Ding F. Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digit. Signal Process. 2010, 20(3):750-762.
52. Li J.H., Ding F., Yang G.W. Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 2012, 55(3-4):442-450.
53. Wang W., Ding F., Dai J.Y. Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 2012, 36(5):1842-1853.
54. Ding F. Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 2013, 37(4):1694-1704.
55. Ding F. Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 2013, 37(7):4798-4808.
56. Ding F. Coupled-least-squares identification for multivariable systems. IET Control Theor. Appl. 2013, 7(x). 10.1049/iet-cta.2012.0171.
57. Ding F. Decomposition based fast least squares algorithm for output error systems. Signal Process. 2013, 93(5):1235-1242.
58. Ding F., Gu Y. Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay. Circuits Syst. Signal Process. 2013, 32(x). 10.1007/s00034-012-9463-5.
59. F. Ding, Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle, IET Control Theor. Appl. 7 (x) (2013), http://dx.doi.org/10.1049/iet-cta.2012.0313.