Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model

Nonlinear Dynamics

Volumn 72, Issue 4, 2013, Pages 865-871

  Chen, Jing ^a,b   Zhang, Yan ^c   Ding, Ruifeng ^a  

^a JIANGNAN UNIVERSITY   (China)

^b Wuxi Professional College of Science and Technology   (China)

^c WUXI INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Auxiliary model; Iterative algorithm; Nonlinear system; Parameter estimation; Recursive identification; Stochastic gradient

Indexed keywords

AUTOREGRESSIVE MOVING AVERAGE; AUXILIARY MODELS; ITERATIVE ALGORITHM; ITERATIVE IDENTIFICATION; RECURSIVE IDENTIFICATION; SIMULATION EXAMPLE; STOCHASTIC GRADIENT; STOCHASTIC GRADIENT ALGORITHMS;

ALGORITHMS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION;

ITERATIVE METHODS;

EID: 84878554517     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0758-2     Document Type: Article

References (38)

1. Olson, C.C., Nichols, J.M., Virgin, L.N.: Parameter estimation for chaotic systems using a geometric approach: theory and experiment. Nonlinear Dyn. 70(1), 381-391 (2012). doi: 10.1007/s11071-012-0461-8
2. Yin, Y.Y., Zivanovic, S., Li, D.X.: Displacement modal identification method of elastic system under operational condition. Nonlinear Dyn. 70(2), 1407-1420 (2012). doi: 10.1007/s11071-012-0543-7
3. j =E over reflexive and anti-reflexive matrices. Int. J. Control. Autom. Syst. 9(1), 118-124 (2011)
4. Chen, W.H., Li, D.X., Lu, X.M.: Impulsive functional observers for linear systems. Int. J. Control. Autom. Syst. 9(5), 987-992 (2011)
5. Liu, Y.J., Xiao, Y.S., Zhao, X.L.: Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477-1483 (2009)
6. Ding, F., Shi, Y., Chen, T.: Performance analysis of estimation algorithms of non-stationary ARMA processes. IEEE Trans. Signal Process. 54(3), 1041-1053 (2006)
7. Ding, F., Liu, X.P., Shi, Y.: Convergence analysis of estimation algorithms of dual-rate stochastic systems. Appl. Math. Comput. 176(1), 245-261 (2006)
8. Ding, J., Ding, F.: The residual based extended least squares identification method for dual-rate systems. Comput. Math. Appl. 56(6), 1479-1487 (2008)
9. Ding, J., Han, L.L., Chen, X.M.: Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Model. 51(5-6), 527-536 (2010)
10. Ding, F., Chen, T., Iwai, Z.: Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM J. Control Optim. 45(6), 2257-2276 (2006)
11. Ding, F., Shi, Y., Chen, T.: Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dyn. 45(1-2), 31-43 (2006)
12. Ding, F., Yang, H.Z., Liu, F.: Performance analysis of stochastic gradient algorithms under weak conditions. Sci. China Ser. F 51(9), 1269-1280 (2008)
13. 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. Hum. 38(4), 966-975 (2008)
14. Ding, F., Chen, T.: A gradient based adaptive control algorithm for dual-rate systems. Asian J. Control 8(4), 314-323 (2006)
15. Ding, J., Shi, Y., Wang, H.G., Ding, F.: A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems. Digit. Signal Process. 20(4), 1238-1247 (2010)
16. Liu, Y.J., Sheng, J., Ding, R.F.: Convergence of stochastic gradient algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615-2627 (2010)
17. Ding, F., Chen, T.: Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1-14 (2007)
18. Ding, F., Liu, X.P., Liu, G.: Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 89(10), 1883-1890 (2009)
19. Han, L.L., Ding, F.: Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process. 19(4), 545-554 (2009)
20. Ding, F.: Several multi-innovation identification methods. Digit. Signal Process. 20(4), 1027-1039 (2010)
21. Xie, L., Yang, H.Z., Ding, F.: Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl. 4(5), 784-794 (2010)
22. Liu, Y.J., Yu, L., Ding, F.: Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 29(4), 649-667 (2010)
23. Ding, F., Liu, X.P., Liu, G.: Multi-innovation least squares identification for system modeling. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(3), 767-778 (2010)
24. Ding, F., Chen, T.: Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans. Autom. Control 50(9), 1436-1441 (2005)
25. Ding, F., Chen, T.: Combined parameter and output estimation of dual-rate systems using an auxiliary model. Automatica 40(10), 1739-1748 (2004)
26. Wang, D.Q., Chu, Y.Y., Ding, F.: Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems. Comput. Math. Appl. 59(9), 3092-3098 (2010)
27. Wang, D.Q., Chu, Y.Y., Yang, G.W., Ding, F.: Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems. Math. Comput. Model. 52(1-2), 309-317 (2010)
28. Ding, F., Chen, T.: Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Autom. Control 50(8), 1216-1221 (2005)
29. Ding, F., Chen, T.: Iterative least squares solutions of coupled Sylvester matrix equations. Syst. Control Lett. 54(2), 95-107 (2005)
30. Ding, F., Chen, T.: Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479-1489 (2005)
31. Ding, F., Shi, Y., Chen, T.: Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 56(5), 373-380 (2007)
32. Wang, D.Q., Ding, F.: Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Comput. Math. Appl. 56(12), 3157-3164 (2008)
33. Ding, F., Liu, X.P., Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215-238 (2011)
34. Wang, D.Q., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182-1189 (2011)
35. Chen, J., Zhang, Y., Ding, R.F.: Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Math. Comput. Model. 52(9-10), 1428-1434 (2010)
36. Wang, D.Q., Yang, G.W., Ding, R.F.: Gradient-based iterative parameter estimation for Box-Jenkins systems. Comput. Math. Appl. 60(5), 1200-1208 (2010)
37. Chen, J., Wang, X.P.: Multi-innovation generalized extended stochastic gradient algorithm for multi-input multi-output nonlinear Box-Jenkins systems based on the auxiliary model. In: Lecture Notes in Computer Science, pp. 136-146. Springer, Berlin (2010)
38. Chen, J., Ding, F.: Least squares and stochastic gradient parameter estimation for multivariable nonlinear Box-Jenkins models based on the auxiliary model and multi-innovation theory. Eng. Comput. 29(8), 907-921 (2012)