Parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search

Applied Mathematics and Computation

Volumn 219, Issue 5, 2012, Pages 2498-2505

  Chen, Jing ^a,b   Lu, Xianling ^a   Ding, Rui ^a  

^a JIANGNAN UNIVERSITY   (China)

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

Author keywords

Forgetting factor; Identification model; Parameter estimation; Preload nonlinearity; Stochastic gradient; The finite impulse response model

Indexed keywords

FINITE IMPULSE RESPONSE MODEL; FORGETTING FACTORS; IDENTIFICATION MODEL; NON-LINEARITY; STOCHASTIC GRADIENT;

PARAMETER ESTIMATION; SWITCHING FUNCTIONS;

NONLINEAR SYSTEMS;

EID: 84868210882     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.08.085     Document Type: Article

References (79)

1. X.G. Liu, and J. Lu Least squares based iterative identification for a class of multirate systems Automatica 46 3 2010 549 554
2. Y.J. Liu, J. Sheng, and R.F. Ding Convergence of stochastic gradient algorithm for multivariable ARX-like systems Computers and Mathematics with Applications 59 8 2010 2615 2627
3. 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
4. B. Yu, H. Fang, Y. Lin, and Y. Shi Identification of Hammerstein output-error systems with two-segment nonlinearities: algorithm and applications Journal of Control and Intelligent Systems 38 4 2010 194 201
5. F. Ding, Y.J. Liu, and B. Bao 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 Engineering 226 1 2012 43 55
6. Y. Shi, and T. Chen Optimal design of multi-channel transmultiplexers with stopband energy and passband magnitude constraints IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 50 9 2003 659 662
7. Y. Shi, F. Ding, and T. Chen Multirate crosstalk identification in xDSL systems IEEE Transactions on Communications 54 10 2006 1878 1886 (Pubitemid 44637822)
8. Y. Shi, and H. Fang Kalman filter based identification for systems with randomly missing measurements in a network environment International Journal of Control 83 3 2010 538 551
9. infin filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains Automatica 48 1 2012 159 166
10. 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
11. F. Ding, and T. Chen A gradient based adaptive control algorithm for dual-rate systems Asian Journal of Control 8 4 2006 314 323
12. 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 (Pubitemid 350171715)
13. J.B. Zhang, F. Ding, and Y. Shi Self-tuning control based on multi-innovation stochastic gradient parameter estimation Systems and Control Letters 58 1 2009 69 75
14. X.G. Liu, and Y.X. Zhou High-purity control of internal thermally coupled distillation columns based on the nonlinear wave model Journal of Process Control 21 6 2011 920 926
15. X.G. Liu, C.Y. Wang, and L. Cong Adaptive robust generic model control of high-purity internal thermally coupled distillation column Chemical Engineering and Technology 34 1 2011 111 118
16. X.G. Liu, and C.Y. Wang Adaptive generalised predictive control of high purity internal thermally coupled distillation column Canadian Journal of Chemical Engineering 90 2 2012 420 428
17. 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
18. 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
19. F. Ding, and T. Chen Performance analysis of multi-innovation gradient type identification methods Automatica 43 1 2007 1 14 (Pubitemid 44792035)
20. F. Ding, X.P. Liu, and G. Liu Identification methods for Hammerstein nonlinear systems Digital Signal Processing 21 2 2011 215 238
21. F. Ding Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling Applied Mathematical Modelling 2012 10.1016/j.apm.2012.04.039
22. 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
23. 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 and Mathematics with Applications 62 11 2011 4170 4177
24. 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 55 3-4 2012 442 450
25. W. Wang, J.H. Li, and R.F. Ding Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models International Journal of Computer Mathematics 88 16 2011 3458 3467
26. W. Wang, F. Ding, and J.Y. Dai Maximum likelihood least squares identification for systems with autoregressive moving average noise Applied Mathematical Modelling 36 5 2012 1842 1853
27. F. Ding, G. Liu, and X.P. Liu Parameter estimation with scarce measurements Automatica 47 8 2011 1646 1655
28. Y. Gu, and F. Ding Auxiliary model based least squares identification method for a state space model with a unit time-delay Applied Mathematical Modelling 36 12 2012 5773 5779
29. F. Ding, and Y. Gu Performance analysis of the auxiliary model based least squares identification algorithm for one-step state delay systems International Journal of Computer Mathematics 2012 698008 10.1080/00207160.2012
30. F. Ding, and Y. Gu Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay circuits Systems and Signal Processing 2012 10.1007/s00034-012-9463-5
31. 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 (Pubitemid 40970287)
32. 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
33. L.F. Zhuang, and F. Pan Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models Applied Mathematical Modelling 36 8 2012 3454 3463
34. F. Ding, and T. Chen Identification of Hammerstein nonlinear ARMAX systems Automatica 41 9 2005 1479 1489 (Pubitemid 41000116)
35. 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
36. D.Q. Wang, and F. Ding Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems Computers and Mathematics with Applications 56 12 2008 3157 3164
37. J. Ding, F. Ding, X.P. Liu, and G. Liu Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data IEEE Transactions on Automatic Control 56 11 2011 2677 2683
38. J. Ding, and F. Ding Bias compensation based parameter estimation for output error moving average systems International Journal of Adaptive Control and Signal Processing 25 12 2011 1100 1111
39. F. Ding, and Y.S. Xiao A finite-data-window least squares algorithm with a forgetting factor for dynamical modeling Applied Mathematics and Computation 186 1 2007 184 192 (Pubitemid 46435609)
40. H.Y. Hu, and F. Ding An iterative least squares estimation algorithm for controlled moving average systems based on matrix decomposition Applied Mathematics Letters 2012 10.1016/j.aml.2012.06.027
41. 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 (Pubitemid 40466884)
42. 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 (Pubitemid 43280579)
43. J. Ding, L.L. Han, and X.M. Chen Time series AR modeling with missing observations based on the polynomial transformation Mathematical and Computer Modelling 51 5-6 2010 527 536
44. F. Ding, X.P. 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
45. 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
46. F. Ding, G. Liu, and X.P. Liu Partially coupled stochastic gradient identification methods for non-uniformly sampled systems IEEE Transactions on Automatic Control 55 8 2010 1976 1981
47. Y.S. Xiao, G.L. Song, Y.W. Liao, and R.F. Ding Multi-innovation stochastic gradient parameter estimation for input nonlinear controlled autoregressive models International Journal of Control, Automation, and Systems 10 3 2012 639 643
48. Y. Zhang, and G.M. Cui Bias compensation methods for stochastic systems with colored noise Applied Mathematical Modelling 35 4 2011 1709 1716
49. Y. Zhang Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods Mathematical and Computer Modelling 53 9-10 2011 1810 1819
50. 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 (Pubitemid 41410122)
51. F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Systems and Control Letters 54 2 2005 95 107
52. F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM Journal on Control and Optimization 44 6 2006 2269 2284 (Pubitemid 44775259)
53. F. Ding, X.P. 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 (Pubitemid 351215477)
54. L. Xie, and J. Ding Gradient based iterative solutions for general linear matrix equations Computers and Mathematics with Applications 58 7 2009 1441 1448
55. J. Ding, and Y.J. Liu Iterative solutions to matrix equations of form AiXBi = Fi Computers and Mathematics with Applications 59 11 2010 3500 3507
56. F. Ding Transformations between some special matrices Computers and Mathematics with Applications 59 8 2010 2676 2695
57. 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 217 5 2010 2191 2199
58. 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
59. F. Ding, and T. Chen Combined parameter and output estimation of dual-rate systems using an auxiliary model Automatica 40 10 2004 1739 1748
60. 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 (Pubitemid 41388188)
61. 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
62. F. Ding, X.P. 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
63. Y.J. Liu, and L. Xie 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
64. 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
65. F. Ding, H.B. Chen, and M. Li Multi-innovation least squares identification methods based on the auxiliary model for MISO systems Applied Mathematics and Computation 187 2 2007 658 668 (Pubitemid 46627857)
66. Y.J. Liu, and L. Yu Multi-innovation extended stochastic gradient algorithm and its performance analysis Circuits, Systems and Signal Processing 29 4 2010 649 667
67. F. Ding, X.P. Liu, and G. Liu Multi-innovation least squares identification for linear and pseudo-linear regression models IEEE Transactions on Systems Man and Cybernetics Part B: Cybernetics 40 3 2010 767 778
68. L. Xie, and Y.J. Liu Modeling and identification for non-uniformly periodically sampled-data systems IET Control Theory and Applications 4 5 2010 784 794
69. F. Ding Several multi-innovation identification methods Digital Signal Processing 20 4 2010 1027 1039
70. H.Q. Han, and L. Xie Hierarchical least squares based iterative identification for multivariable systems with moving average noises Mathematical and Computer Modelling 51 9-10 2010 1213 1220
71. Z.N. Zhang, F. Ding, and X.G. Liu Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems Computers and Mathematics with Applications 61 3 2011 672 682
72. Y.J. Liu, F. Ding, and Y. Shi Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle Circuits Systems and Signal Processing 2012 10.1007/s00034-012-9421-2
73. 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
74. J. Chen, X.P. Wang, and R.F. Ding Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities Applied Mathematical Modelling 36 1 2012 238 243
75. F. Ding, Y. Shi, and T. Chen Auxiliary model based least-squares identification methods for Hammerstein output-error systems Systems and Control Letters 56 5 2007 373 380 (Pubitemid 46435731)
76. Y.S. Xiao, and N. Yue Parameter estimation for nonlinear dynamical adjustment models Mathematical and Computer Modelling 54 5-6 2011 1561 1568
77. J. Ding, F. Ding, and S. Zhang Parameter identification of multi-input, single-output systems based on FIR models and least squares principle Applied Mathematics and Computation 197 1 2008 297 305 (Pubitemid 351215497)
78. L.L. Han, and F. Ding Identification for multirate multi-input systems using the multi-innovation identification theory Computers and Mathematics with Applications 57 9 2009 1438 1449
79. L.L. Han, and J. Sheng Auxiliary models based recursive least squares identification for multirate multi-input systems Mathematical and Computer Modelling 50 7-8 2009 1100 1106