Parameter estimation methods for nonlinear systems

Applied Mathematics and Computation

Volumn 219, Issue 9, 2013, Pages 4278-4287

  Li, Junhong ^a,b   Ding, Rui ^b  

^a NANTONG UNIVERSITY   (China)

^b JIANGNAN UNIVERSITY   (China)

Author keywords

Gradient iteration; Newton iteration; Nonlinear systems; Parameter estimation; System modeling

Indexed keywords

ESTIMATION METHODS; GRADIENT BASED ITERATIVE ALGORITHMS; GRADIENT ITERATION; GRADIENT SEARCH; ITERATIVE ALGORITHM; MODEL TRANSFORMATION; NEWTON ITERATIONS; NON-LINEAR OPTIMIZATION PROBLEMS; NONLINEAR SYSTEM MODELING; NUMERICAL EXAMPLE; PARAMETER ESTIMATION METHOD; SYSTEM MODELING;

ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; NEWTON-RAPHSON METHOD; OPTIMIZATION; PARAMETER ESTIMATION;

NONLINEAR SYSTEMS;

EID: 84871219614     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.09.045     Document Type: Article

References (39)

1. 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
2. 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
3. J. Ding, and F. Ding Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data IEEE Transactions on Automatic Control 56 11 2011 2677 2683
4. 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
5. 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
6. TD = F Applied Mathematics and Computation 217 5 2010 2191 2199
7. M. Dehghan, and M. Hajarian An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation Applied Mathematics and Computation 202 2 2008 571 588
8. A 2X 2B 2 = C Mathematical and Computer Modelling 49 9-10 2009 1937 1959
9. M. Dehghan, and M. Hajarian Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations Applied Mathematics Letters 24 4 2011 444 449
10. F. Ding System Identification - New Theory and Methods 2012 Science Press Beijing
11. F. Ding, X.P. 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
12. F. Ding Several multi-innovation identification methods Digital Signal Processing 20 4 2010 1027 1039
13. 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
14. 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
15. F. Ding, X.P. Liu, and G. Liu Identification methods for Hammerstein nonlinear systems Digital Signal Processing 21 2 2011 215 238
16. Y.J. Liu, and D.Q. Wang Least squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data Digital Signal Processing 20 5 2010 1458 1467
17. 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
18. F. Ding, P.X. Liu, and G. Liu Multi-innovation least squares identification for system modelling IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40 3 2010 767 778
19. F. Ding, and J. Ding Least squares parameter estimation for systems with irregularly missing data International Journal of Adaptive Control and Signal Processing 24 7 2010 540 553
20. 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
21. 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 89 15 2012 2019 2028
22. F. Ding System identification - Part A: Introduction to the identification Journal of Nanjing University of Information Science and Technology (Natural Science Edition) 3 1 2011 1 22
23. F. Ding System identification - Part B: Basic models for system description Journal of Nanjing University of Information Science and Technology (Natural Science Edition) 3 2 2011 97 117
24. F. Ding System identification - Part C: Identification accuracy and basic problems Journal of Nanjing University of Information Science and Technology (Natural Science Edition) 3 3 2011 193 226
25. F. Ding System identification - Part D: Auxiliary model identification idea and methods Journal of Nanjing University of Information Science and Technology (Natural Science Edition) 3 4 2011 289 318
26. F. Ding System identification - Part E: Iterative search principle and identification methods Journal of Nanjing University of Information Science and Technology (Natural Science Edition) 3 6 2011 481 510
27. 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
28. 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
29. F. Ding, and T. Chen Identification of Hammerstein nonlinear ARMAX systems Automatica 41 9 2005 1479 1489
30. 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
31. J. Vörös Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities Systems & Control Letters 56 2 2007 99 105
32. J.H. Li, F. Ding, Parameter fitting for nonlinear systems, in: The 23th Chinese Control and Decision Conference (2011 CCDC), May 23- 25, 2011, Mianyang, China, pp. 1085-1090.
33. 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
34. F. Ding Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling Applied Mathematical Modelling 37 2013 10.1016/j.apm.2012.04.039
35. 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 62 11 2011 4170 4177
36. 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 32 2013 10.1007/s00034-012-9463-5
37. J.H. Li Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration Applied Mathematics Letters 26 1 2013 91 96
38. J. Nocedal, and S.J. Wright Numerical Optimization 2000 Springer New York
39. J.H. Li, R.F. Ding, and Y. Yang Iterative parameter identification methods for nonlinear functions Applied Mathematical Modelling 26 6 2012 2739 2750