Multi-innovation stochastic gradient parameter estimation for input nonlinear controlled autoregressive models

International Journal of Control, Automation and Systems

Volumn 10, Issue 3, 2012, Pages 639-643

  Xiao, Yongsong ^a   Song, Guanglei ^b   Liao, Yuwu ^c   Ding, Ruifeng ^a  

^a JIANGNAN UNIVERSITY   (China)

^b WUXI INSTITUTE OF TECHNOLOGY   (China)

^c HUBEI UNIVERSITY OF ARTS AND SCIENCE   (China)

Author keywords

Hammerstein model; Multi innovation identification; Parameter estimation; Recursive identification; Stochastic gradient; System modeling

Indexed keywords

HAMMERSTEIN MODEL; MULTI-INNOVATION IDENTIFICATION; RECURSIVE IDENTIFICATION; STOCHASTIC GRADIENT; SYSTEM MODELING;

COMPUTER APPLICATIONS; CONTROL;

PARAMETER ESTIMATION;

EID: 84865991803     PISSN: 15986446     EISSN: 20054092     Source Type: Journal    
DOI: 10.1007/s12555-012-0322-8     Document Type: Article

References (49)

1. D. Q. Wang and F. Ding, "Extended stochastic gradient identification algorithms for Hammersteinwiener ARMAX systems," Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3157-3164, 2008.
2. J. Chen, Y. Zhang, and R. F. Ding, "Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems," Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1428-1434, 2010.
3. D. Q. Wang, Y. Y. Chu, and F. Ding, "Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems," Computers & Mathematics with Applications, vol. 59, no. 9, pp. 3092-3098, 2010.
4. D. Q. Wang, Y. Y. Chu, G. W. Yang, and F. Ding, "Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems," Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 309-317, 2010.
5. F. Ding and T. Chen, "Combined parameter and output estimation of dual-rate systems using an auxiliary model," Automatica, vol. 40, no. 10, pp. 1739-1748, 2004.
6. F. Ding and T. Chen, "Identification of dual-rate systems based on finite impulse response models," International Journal of Adaptive Control and Signal Processing, vol. 18, no. 7, pp. 589-598, 2004.
7. F. Ding and T. Chen, "Parameter estimation of dual-rate stochastic systems by using an output error method," IEEE Trans. on Automatic Control, vol. 50, no. 9, pp. 1436-1441, 2005. (Pubitemid 41388188)
8. F. Ding, P. X. Liu, and G. Liu, "Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises," Signal Processing, vol. 89, no. 10, pp. 1883-1890, 2009.
9. Y. J. Liu, L. Xie, and F. Ding, "An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems," Proc. of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 223, no. 4, pp. 445-454, 2009.
10. F. Ding and J. Ding, "Least squares parameter estimation with irregularly missing data," International Journal of Adaptive Control and Signal Processing, vol. 24, no. 7, pp. 540-553, 2010.
11. F. Ding, G. Liu, and X. P. Liu, "Parameter estimation with scarce measurements," Automatica, vol. 47, no. 8, pp. 1646-1655, 2011.
12. F. Ding, "Several multi-innovation identification methods," Digital Signal Processing, vol. 20, no. 4, pp. 1027-1039, 2010.
13. F. Ding and T. Chen, "Performance analysis of multi- innovation gradient type identification methods," Automatica, vol. 43, no. 1, pp. 1-14, 2007. (Pubitemid 44792035)
14. Y. J. Liu, Y. S. Xiao, and X. L. Zhao, "Multiinnovation stochastic gradient algorithm for multiple- input single-output systems using the auxiliary model," Applied Mathematics and Computation, vol. 215, no. 4, pp. 1477-1483, 2009.
15. L. Xie, H. Z. Yang, and F. Ding, "Modeling and identification for non-uniformly periodically sampled- data systems," IET Control Theory & Applications, vol. 4, no. 5, pp. 784-794, 2010.
16. L. L. Han and F. Ding, "Multi-innovation stochastic gradient algorithms for multi-input multi-output systems," Digital Signal Processing, vol. 19, no. 4, pp. 545-554, 2009.
17. F. Ding and T. Chen, "Hierarchical least squares identification methods for multivariable systems," IEEE Trans. on Automatic Control, vol. 50, no. 3, pp. 397-402, 2005. (Pubitemid 40448592)
18. H. Q. Han, L. Xie, F. Ding, and X. G. Liu, "Hierarchical least squares based iterative identification for multivariable systems with moving average noises," Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1213-1220, 2010.
19. F. Ding, L. Qiu, and T. Chen, "Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems," Automatica, vol. 45, no. 2, pp. 324-332, 2009.
20. J. Ding, F. Ding, X. P. Liu, and G. Liu, "Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data," IEEE Trans. on Automatic Control, vol. 56, no. 11, pp. 2677-2683, 2011.
21. Y. Zhang and G. M. Cui, "Bias compensation methods for stochastic systems with colored noise," Applied Mathematical Modelling, vol. 35, no. 4, pp. 1709-1716, 2011.
22. Y. Zhang, "Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods," Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 1810-1819, 2011.
23. J. Ding and F. Ding, "Bias compensation based parameter estimation for output error moving average systems," International Journal of Adaptive Control and Signal Processing, vol. 25, no. 12, pp. 1100-1111, 2011.
24. F. Ding, P. X. Liu, and G. Liu, "Gradient based and least-squares based iterative identification methods for OE and OEMA systems," Digital Signal Processing, vol. 20, no. 3, pp. 664-677, 2010.
25. Y. S. Xiao, Y. Zhang, J. Ding, and J. Y. Dai, "The residual based interactive least squares algorithms and simulation studies," Computers & Mathematics with Applications, vol. 58, no. 6, pp. 1190-1197, 2009.
26. L. Y. Wang, L. Xie, and X. F. Wang, "The residual based interactive stochastic gradient algorithms for controlled moving average models," Applied Mathematics and Computation, vol. 211, no. 2, pp. 442-449, 2009.
27. Y. J. Liu, D. Q. Wang, and F. Ding, "Least-squares based iterative algorithms for identifying Box- Jenkins models with finite measurement data," Digital Signal Processing, vol. 20, no. 5, pp. 1458-1467, 2010.
28. D. Q. Wang, G. W. Yang, and R. F. Ding, "Gradientbased iterative parameter estimation for Box- Jenkins systems," Computers & Mathematics with Applications, vol. 60, no. 5, pp. 1200-1208, 2010.
29. F. Ding, P. X. Liu, and G. Liu, "Identification methods for Hammerstein nonlinear systems," Digital Signal Processing, vol. 21, no. 2, pp. 215-238, 2011.
30. W. H. Chen, D. X. Li, and X. M. Lu, "Impulsive functional observers for linear systems," International Journal of Control, Automation, and Systems, vol. 9, no. 5, pp. 987-992, 2011.
31. D. Q. Wang and F. Ding, "Least squares based and gradient based iterative identification for Wiener nonlinear systems," Signal Processing, vol. 91, no. 5, pp. 1182-1189, 2011.
32. M. Dehghan and M. Hajarian, "Solving the generalized Sylvester matrix equation ∑AiXBi + ∑CjYDj = E over reflexive and anti-reflexive matrices," International Journal of Control, Automation, and Systems, vol. 9, no. 1, pp. 118-124, 2011.
33. L. Xie, J. Ding, and F. Ding, "Gradient based iterative solutions for general linear matrix equations," Computers & Mathematics with Applications, vol. 58, no. 7, pp. 1441-1448, 2009.
34. J. Ding, Y. J. Liu, and F. Ding, "Iterative solutions to matrix equations of form AiXBi=Fi," Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3500-3507, 2010.
35. L. Xie, Y. J. Liu, and H. Z. Yang, "Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F," Applied Mathematics and Computation, vol. 217, no. 5, pp. 2191-2199, 2010.
36. F. Ding, "Transformations between some special matrices," Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2676-2695, 2010.
37. F. Ding, P. X. Liu, and J. Ding, "Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle," Applied Mathematics and Computation, vol. 197, no. 1, pp. 41-50, 2008. (Pubitemid 351215477)
38. F. Ding, G. Liu, and X.P. Liu, "Partially coupled stochastic gradient identification methods for nonuniformly sampled systems," IEEE Trans. on Automatic Control, vol. 55, no. 8, pp. 1976-1981, 2010.
39. Y. S. Xiao, D. Q. Wang, and F. Ding, "The residual based ESG algorithm and its performance analysis," Journal of the Franklin Institute - Engineering and Applied Mathematics, vol. 347, no. 2, pp. 426-437, 2010.
40. Y. S. Xiao, F. Ding, Y. Zhou, M. Li, and J.Y. Dai, "On consistency of recursive least squares identification algorithms for controlled auto-regression models," Applied Mathematical Modelling, vol. 32, no. 11, pp. 2207-2215, 2008.
41. Y. S. Xiao, H. B. Chen, and F. Ding, "Identification of multi-input systems based on the correlation techniques," International Journal of Systems Science, vol. 42, no. 1, pp. 139-147, 2011.
42. Y. W. Liao, L. Yu, and L. L. Xiang, "Multiinnovation stochastic gradient algorithm for Hammerstien nonlinear ARX systems," Proc. of the Fourth International Conference on Genetic and Evolutionary Computing, Shenzhen, China, pp. 868-871, December 13-15, 2010.
43. F. Ding and T. Chen, "Identification of Hammerstein nonlinear ARMAX systems," Automatica, vol. 41, no. 9, pp. 1479-1489, 2005. (Pubitemid 41000116)
44. J. H. Li and F. Ding, "Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique," Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4170-4177, 20011.
45. J. H. Li, F. Ding, and G. W. Yang, "Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems," Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 442-450, 2012.
46. F. Ding, Y. J. Liu, and B. Bao, "Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems," Proc. of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 226, no. 1, pp. 43-55, 2012.
47. F. Ding and T. Chen, "Hierarchical gradient-based identification of multivariable discrete-time systems," Automatica, vol. 41, no. 2, pp. 315-325, 2005. (Pubitemid 41536582)
48. F. Ding, P. X Liu, and G. Liu, "Multi-innovation least squares identification for linear and pseudolinear regression models," IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 3, pp. 767-778, 2010.
49. F. Ding, X. P. Liu, and H. Z. Yang, "Parameter identification and intersample output estimation for dual-rate systems," IEEE Trans. on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 38, no. 4, pp. 966-975, 2008.