Hierarchical least squares based iterative estimation algorithm for multivariable Box-Jenkins-like systems using the auxiliary model

Applied Mathematics and Computation

Volumn 218, Issue 9, 2012, Pages 5580-5587

  Zhang, Zhening ^a   Jia, Jie ^b   Ding, Ruifeng ^a,b  

^a JIANGNAN UNIVERSITY   (China)

^b NANCHANG HANGKONG UNIVERSITY   (China)

Author keywords

Auxiliary model identification; Hierarchical identification; Least squares; Multivariable Box Jenkins like model; Parameter estimation; System modelling

Indexed keywords

AUXILIARY MODELS; HIERARCHICAL IDENTIFICATION; LEAST SQUARE; MULTI VARIABLES; SYSTEM MODELLING;

ALGORITHMS; ESTIMATION; HIERARCHICAL SYSTEMS; IDENTIFICATION (CONTROL SYSTEMS); ITERATIVE METHODS; MULTIVARIABLE SYSTEMS;

PARAMETER ESTIMATION;

EID: 83555161557     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.11.051     Document Type: Article

References (72)

1. Y. Zhang, and G.M. Cui Bias compensation methods for stochastic systems with colored noise Applied Mathematical Modelling 35 4 2011 1709 1716
2. 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 32 11 2008 2207 2215
3. H. Habbi, M. Kidouchea, and M. Zelmat Data-driven fuzzy models for nonlinear identification of a complex heat exchanger Applied Mathematical Modelling 35 3 2011 1470 1482
4. A. Zymnis, S. Boyd, and D. Gorinevsky Mixed linear system estimation and identification Signal Processing 90 3 2010 966 971
5. M. Dehghan, and M. Hajarian An efficient algorithm for solving general coupled matrix equations and its application Mathematical and Computer Modelling 51 9-10 2010 1118 1134
6. F. Ding, and T. Chen Gradient based iterative algorithms for solving a class of matrix equations IEEE Transactions on Automatic Control 50 8 2005 1216 1221
7. F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Systems & Control Letters 54 2 2005 95 107
8. F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM Journal on Control and Optimization 44 6 2006 2269 2284
9. 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 197 1 2008 41 50
10. L. Xie, J. Ding, and F. Ding Gradient based iterative solutions for general linear matrix equations Computers & Mathematics with Applications 58 7 2009 1441 1448
11. F. Ding Transformations between some special matrices Computers & Mathematics with Applications 59 8 2010 2676 2695
12. J. Ding, Y.J. Liu, and F. Ding Iterative solutions to matrix equations of form AiXBi=Fi Computers & Mathematics with Applications 59 11 2010 3500 3507
13. TD=F Applied Mathematics and Computation 217 5 2010 2191 2199
14. Y. N Cao, and Z.Q. Liu Signal frequency and parameter estimation for power systems using the hierarchical identification principle Mathematical and Computer Modelling 52 5-6 2010 854 861
15. Y.Y. Fu, C.J. Wu, J.T. Jeng, and C.N. Ko Identification of MIMO systems using radial basis function networks with hybrid learning algorithm Applied Mathematics and Computation 213 1 2009 184 196
16. H. Peng, G. Kitagawa, J. Wu, and K. Ohtsu Multivariable RBF-ARX model-based robust MPC approach and application to thermal power plant Applied Mathematical Modelling 35 7 2011 3541 3551
17. M. Ahmadia, and H. Mojallali Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials Applied Mathematical Modelling 35 4 2011 1969 1982
18. L.L. Han, and F. Ding Multi-innovation stochastic gradient algorithms for multi-input multi-output systems Digital Signal Processing 19 4 2009 545 554
19. F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. in: Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2011, in press. doi:10.1177/0959651811409491
20. L.L. Xiang, L.B. Xie, Y.W. Liao, and R.F. Ding Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model Mathematical and Computer Modelling 52 5-6 2010 918 924
21. B. Bao, Y.Q. Xu, J. Sheng, and R.F. Ding Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data Mathematical and Computer Modelling 53 9-10 2011 1664 1669
22. Y.J. Liu, J. Sheng, and R.F. Ding Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems Computers & Mathematics with Applications 59 8 2010 2615 2627
23. D.Q. Wang Least squares-based recursive and iterative estimation for output error moving average (OEMA) systems using data filtering IET Control theory and Applications 5 14 2011 1648 1657
24. D.Q. Wang, and F. Ding Input-output data filtering based recursive least squares parameter estimation for CARARMA systems Digital Signal Processing 20 4 2010 991 999
25. 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 20 3 2010 664 677
26. F. Ding, P.X. Liu, and G. Liu Identification methods for Hammerstein nonlinear systems Digital Signal Processing 21 2 2011 215 238
27. 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 59 9 2010 3092 3098
28. 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 52 1-2 2010 309 317
29. D.Q. Wang, and F. Ding Least squares based and gradient based iterative identification for Wiener nonlinear systems Signal Processing 91 5 2011 1182 1189
30. F. Ding, and T. Chen Identification of Hammerstein nonlinear ARMAX systems Automatica 41 9 2005 1479-148
31. F. Ding, Y. Shi, and T. Chen Auxiliary model based least-squares identification methods for Hammerstein output-error systems Systems & Control Letters 56 5 2007 373 380
32. F. Ding, Y. Shi, and T. Chen Gradient-based identification methods for Hammerstein nonlinear ARMAX models Nonlinear Dynamics 45 1-2 2006 31 43
33. J. Chen, Y. Zhang, and R.F. Ding Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems Mathematical and Computer Modelling 52 9-10 2010 1428 1434
34. D.Q. Wang, and F. Ding Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems Computers & Mathematics with Applications 56 12 2008 3157 3164
35. J. Chen, and F. Ding Modified stochastic gradient algorithms with fast convergence rates Journal of Vibration and Control 17 9 2011 1281 1286
36. J. Ding, Y. Shi, H.G. Wang, and F. Ding A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems Digital Signal Processing 20 4 2010 1238 1249
37. F. Ding, P.X. Liu, and H.Z. Yang Parameter identification and intersample output estimation for dual-rate systems IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 38 4 2008 966 975
38. F. Ding, H.Z. Yang, and F. Liu Performance analysis of stochastic gradient algorithms under weak conditions Science in China Series F-Information Sciences 51 9 2008 1269 1280
39. F. Ding, and T. Chen Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data IEEE Transactions on Circuits and Systems-I: Regular Papers 52 3 2005 555 566
40. W. Wang, F. Ding, and J.Y. Dai Maximum likelihood least squares identification for systems with autoregressive moving average noise Applied Mathematical Modelling 36 x 2012 10.1016/j.apm.2011.07.083
41. F. Ding, and T. Chen Performance analysis of multi-innovation gradient type identification methods Automatica 43 1 2007 1 14
42. Y.J. Liu, Y.S. Xiao, and X.L. Zhao Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model Applied Mathematics and Computation 215 4 2009 1477 1483
43. F. Ding, P.X. Liu, and G. Liu Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises Signal Processing 89 10 2009 1883 1890
44. J.B. Zhang, F. Ding, and Y. Shi Self-tuning control based on multi-innovation stochastic gradient parameter estimation Systems & Control Letters 58 1 2009 69 75
45. F. Ding, P. X Liu, and G. Liu Multi-innovation least squares identification for system modeling IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40 3 2010 767 778
46. F. Ding Several multi-innovation identification methods Digital Signal Processing 20 4 2010 1027 1039
47. D.Q. Wang, and F. Ding Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems Digital Signal Processing 20 3 2010 750 762
48. L. Xie, H.Z. Yang, and F. Ding Modeling and identification for non-uniformly periodically sampled-data systems IET Control Theory & Applications 4 5 2010 784 794
49. L.L. Han, and F. Ding Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation Journal of Systems Engineering and Electronics 21 6 2010 1079 1083
50. L.L. Han, and F. Ding Identification for multirate multi-input systems using the multi-innovation identification theory Computers & Mathematics with Applications 57 9 2009 1438 1449
51. Y.J. Liu, L. Yu, and F. Ding Multi-innovation extended stochastic gradient algorithm and its performance analysis Circuits, Systems and Signal Processing 29 4 2010 649 667
52. F. Ding, and T. Chen Combined parameter and output estimation of dual-rate systems using an auxiliary model Automatica 40 10 2004 1739 1748
53. F. Ding, and T. Chen Identification of dual-rate systems based on finite impulse response models International Journal of Adaptive Control and Signal Processing 18 7 2004 589 598
54. F. Ding, and T. Chen Least squares based self-tuning control of dual-rate systems International Journal of Adaptive Control and Signal Processing 18 8 2004 697 714
55. F. Ding, and T. Chen Parameter estimation of dual-rate stochastic systems by using an output error method IEEE Transactions on Automatic Control 50 9 2005 1436 1441
56. F. Ding, and T. Chen Hierarchical identification of lifted state-space models for general dual-rate systems IEEE Transactions on Circuits and Systems-I: Regular Papers 52 6 2005 1179 1187
57. F. Ding, and T. Chen A gradient based adaptive control algorithm for dual-rate systems Asian Journal of Control 8 4 2006 314 323
58. F. Ding, T. Chen, and Z. Iwai Adaptive digital control of Hammerstein nonlinear systems with limited output sampling SIAM Journal on Control and Optimization 45 6 2007 2257 2276
59. F. Ding, L. Qiu, and T. Chen Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems Automatica 45 2 2009 324 332
60. Y.J. Liu, L. Xie, and F. Ding 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 Engineering 223 4 2009 445 454
61. F. Ding, G. Liu, and X.P. Liu Partially coupled stochastic gradient identification methods for non-uniformly sampled systems IEEE Transaction on Automatic Control 55 8 2010 1976 1981
62. F. Ding, and J. Ding Least squares parameter estimation with irregularly missing data International Journal of Adaptive Control and Signal Processing 24 7 2010 540 553
63. F. Ding, G. Liu, and X.P. Liu Parameter estimation with scarce measurements Automatica 47 8 2011 1646 1655
64. L. Xie, H.Z. Yang, and F. Ding Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering Mathematical and Computer Modelling 54 1-2 2011 315 324
65. F. Ding, and T. Chen Hierarchical gradient-based identification of multivariable discrete-time systems Automatica 41 2 2005 315 325
66. F. Ding, and T. Chen Hierarchical least squares identification methods for multivariable systems IEEE Transactions on Automatic Control 50 3 2005 397 402
67. 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 51 9-10 2010 1213 1220
68. Z.N. Zhang, F. Ding, and X.G. Liu Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems Computers & Mathematics with Applications 61 3 2011 672 682
69. 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 20 5 2010 1458 1467
70. D.Q. Wang, G.W. Yang, and R.F. Ding Gradient-based iterative parameter estimation for Box-Jenkins systems Computers & Mathematics with Applications 60 5 2010 1200 1208
71. F. Ding, T. Chen, and L. Qiu Bias compensation based recursive least squares identification algorithm for MISO systems IEEE Transactions on Circuits and Systems-II: Express Briefs 53 5 2006 349 353
72. F. Ding, Y. Shi, and T. Chen Performance analysis of estimation algorithms of non-stationary ARMA processes IEEE Transactions on Signal Processing 54 3 2006 1041 1053