Maximum likelihood forgetting stochastic gradient estimation algorithm for Hammerstein CARARMA systems

Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012

Volumn , Issue , 2012, Pages 2533-2538

  Li, Junhong ^a   Gu, Juping ^a   Ma, Weiguo ^a   Ding, Rui ^b  

^a NANTONG UNIVERSITY   (China)

^b JIANGNAN UNIVERSITY   (China)

Author keywords

Hammerstein models; Maximum likelihood; Parameter estimation; Stochastic gradient

Indexed keywords

CONVERGENCE RATES; FORGETTING FACTORS; GRADIENT SEARCH; HAMMERSTEIN MODEL; IDENTIFICATION PROBLEM; MAXIMUM LIKELIHOOD PRINCIPLE; STOCHASTIC GRADIENT; STOCHASTIC GRADIENT ALGORITHMS; STOCHASTIC GRADIENT ESTIMATION;

MAXIMUM LIKELIHOOD; PARAMETER ESTIMATION;

ALGORITHMS;

EID: 84866690563     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCDC.2012.6244405     Document Type: Conference Paper

References (54)

1. F. Ding, Several multi-innovation identification methods, Digital Signal Processing 20 (4) (2010) 1027-1039.
2. L.L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital Signal Processing 19 (4) (2009) 545-554.
3. J.B. Zhang, F. Ding, Y. Shi, Self-tuning control based on multiinnovation stochastic gradient parameter estimation, Systems & Control Letters 58 (1) (2009) 69-75.
4. F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods, Automatica 43 (1) (2007) 1-14.
5. L.L. Han, F. Ding, Identification for multirate multi-input systems using the multi-innovation identification theory, Computers & Mathematics with Applications 57 (9) (2009) 1438-1449.
6. F. Ding, X.P. Liu, G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal Processing 89 (10) (2009) 1883-1890.
7. Y.J. Liu, L. Yu, F. Ding, Multi-innovation extended stochastic gradient algorithm and its performance analysis, Circuits, Systems and Signal Processing 29 (4) (2010) 649-667.
8. D.Q. Wang, F. Ding, Least squares based and gradient based iterative identification for Wiener nonlinear systems, Signal Processing 91 (5) (2011) 1182-1189.
9. F. Ding, X.P. Liu, G. Liu, Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital Signal Processing 20 (3) (2010) 664-677.
10. F. Ding, Transformations between some special matrices, Computers & Mathematics with Applications 59 (8) (2010) 2676-2695.
11. F. Ding, Y.J. Liu, 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
12. Y.J. Liu, D.Q. Wang, F. Ding, Least-squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data, Digital Signal Processing 20 (5) (2010) 1458-1467.
13. F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM Journal on Control and Optimization 44 (6) (2006) 2269-2284.
14. F. Ding, X.P. Liu, 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.
15. L. Xie, J. Ding, F. Ding, Gradient based iterative solutions for general linear matrix equations, Computers & Mathematics with Applications 58 (7) (2009) 1441-1448.
16. T D=F, Applied Mathematics and Computation 217 (5) (2010) 2191-2199.
17. H.Q. Han, L. Xie, F. Ding, 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.
18. Z.N. Zhang, F. Ding, 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.
19. J. Ding, F. Ding, X.P. Liu, 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.
20. L.L. Han, J. Sheng, F. Ding, Y. Shi, Auxiliary models based recursive least squares identification for multirate multi-input systems, Mathematical and Computer Modelling 50 (7-8) (2009)1100-1106.
21. Y.J. Liu, L. Xie, 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.
22. A. Wills, B. Ninness, S. Gibson, Maximum likelihood estimation of state space models from frequency domain data, IEEE Transactions on Automatic Control 54 (1) (2009) 19-33.
23. A. Hagenblad, L. Ljung, A. Wills. Maximum likelihood identification of Wiener models, Automatica 44 (11) (2008) 2697-2705.
24. Thomas B. Schön, Adrian Wills, Brett Ninness. System identification of nonlinear state-space models, Automatica 47 (1)(2011) 39-49.
25. L. Vanbeylen, R. Pintelon, J. Schoukens, Blind maximum likelihood identification of Hammerstein systems, Automatica 44 (12) (2008) 3139-3146.
26. R. Diversi, R. Guidorzi, U. Soverini, Maximum likelihood identification of noisy input-output models, Automatica 43 (3) (2007) 464-472.
27. H. Habbi, M. Kidouche, M. Zelmat, Data-driven fuzzy models for nonlinear identification of a complex heat exchanger, Applied Mathematical Modelling 35 (3) (2011) 1470-1482.
28. J.H. Li, F. Ding. Parameter fitting for nonlinear systems, The 2011 Chinese Control and Decision Conference (2011 CCDC), May 23-25, 2011, Mianyang, China, pp. 1085-1090.
29. J.H. L, R.F. Ding, Y. Yang, Iterative parameter identification methods for nonlinear functions, Applied Mathematical Modelling 26 (6) (2012) 2739-2750.
30. D.Q. Wang, Y.Y. Chu, F. Ding, Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems, Computers & Mathematics with Applications 59 (9) (2010) 3092-3098.
31. D.Q. Wang, Y.Y. Chu, G.W. Yang, 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.
32. F. Ding, Y. Shi, T. Chen, Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems & Control Letters 56 (5) (2007) 373-380.
33. J.D. Wang, Q.H. Zhang, L. Ljung, Revisiting Hammerstein system identification through the two-stage algorithm for bilinear parameter estimation, Automatica 45 (11) (2009) 2627-2633.
34. F. Ding, X.P. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems, Digital Signal Processing 21 (2) (2011) 215-238.
35. W. Wang, J.H. Li, R.F. Ding, Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models, International Journal of Computer Mathematics 88 (16) (2011) 3458-3467.
36. W. Wang, F. Ding, J.Y. Dai, Maximum likelihood least squares identification for systems with autoregressive moving average noise, Applied Mathematical Modelling 36 (5) (2012) 1842-1853.
37. J.H. Li, F. Ding, 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.
38. J.H. Li, F. Ding, Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique, Computers & Mathematics with Applications 62 (11) (2011) 4170-4177.
39. L. Ljung, T. Söerström, Theory and practice of recursive identification, Cambridge, MA: MIT Press, 1983.
40. G.C. Goodwin, K.S. Sin, Adaptive filtering prediction and control, Englewood Cliffs, New Jersey: Prentice-hall, 1984.
41. L. Xie, H.Z. Yang, 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.
42. F. Ding, L. Qiu, T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica 45 (2) (2009) 324-332.
43. F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements, Automatica 47 (8) (2011) 1646-1655.
44. Ding F, Chen T. Modeling and identification for multirate systems. Acta Automatica Sinica, 2005, 31(1): 105-122
45. F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE Transactions on Automatic Control, 2010, 55(8): 1976-1981.
46. F. Ding, T. Chen, Combined parameter and output estimation of dualrate systems using an auxiliary model, Automatica 40 (10) (2004) 1739-1748.
47. F. Ding, T. Chen, Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica 41 (2) (2005) 315-325.
48. F. Ding, T. Chen, Identification of Hammerstein nonlinear ARMAX systems, Automatica, Vol.41, No.9, 1479-148, 2005.
49. F. Ding, Y. Shi, T. Chen, Gradient-based identification methods for Hammerstein nonlinear ARMAX models, Nonlinear Dynamics 45 (1-2) (2006) 31-43.
50. F. Ding, T. Chen, Hierarchical least squares identification methods for multivariable systems, IEEE Transactions on Automatic Control 50 (3) (2005) 397-402.
51. F. Ding, T. Chen, Gradient based iterative algorithms for solving a class of matrix equations, IEEE Transactions on Automatic Control 50 (8) (2005) 1216-1221.
52. F. Ding, 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.
53. Y.J. Liu, Y.S. Xiao, 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.
54. Y.J. Liu, J. Sheng, R.F. Ding, Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems, Computers & Mathematics with Applications 59 (8) (2010) 2615-2627.