Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems

International Journal of Computer Mathematics

Volumn 89, Issue 15, 2012, Pages 2019-2028

  Ding, Feng ^a   Gu, Ya ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Auxiliary model identification; least squares; parameter estimation; Recursive identification; state space model

Indexed keywords

AUXILIARY MODEL IDENTIFICATIONS; IDENTIFICATION ALGORITHMS; LEAST SQUARE; PERFORMANCE ANALYSIS; RECURSIVE IDENTIFICATION; RECURSIVE LEAST SQUARES ALGORITHMS; SIMULATION EXAMPLE; STATE-SPACE MODELS;

PARAMETER ESTIMATION; RANDOM PROCESSES;

ALGORITHMS;

EID: 84865479577     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160.2012.698008     Document Type: Article

References (49)

1. J. Cai and G.L. Chen, An iterative method for the least squares solutions of the linear matrix equations with some constraint, Int. J. Comput. Math. 88(3) (2011), pp. 634-649.
2. M. Dehghan and M. Hajarian, New iterative method for solving nonlinear equations with fourth-order convergence, Int. J. Comput. Math. 87(4) (2010), pp. 834-839.
3. F. Ding, Several multi-innovation identification methods, Digital Signal Process. 20(4) (2010), pp. 1027-1039.
4. F. Ding, Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling, Appl. Math. Model. (2012), doi:10.1016/j.apm.2012.04.039.
5. F. Ding and T. Chen, Identification of Hammerstein nonlinear ARMAX systems, Automatica 41(9) (2005), pp. 1479-1489.
6. F. Ding and T. Chen, Performance analysis of multi-innovation gradient type identification methods, Automatica 43(1) (2007), pp. 1-14.
7. F. Ding and J. Ding, Least squares parameter estimation with irregularly missing data, Int. J. Adapt. Control Signal Process. 24(7) (2010), pp. 540-553.
8. J. Ding and F. Ding, Bias compensation based parameter estimation for output error moving average systems, Int. J. Adapt. Control Signal Process. 25(12) (2011), pp. 1100-1111.
9. F. Ding,Y. Shi, and T. Chen, A new identification algorithm for multi-input ARX systems, 2005 IEEE International Conference on Mechatronics and Automation, Niagara Fall, Ontario, Canada, July 29-August 1, 2005, pp. 764-769.
10. F. Ding, Y. Shi, and T. Chen, Auxiliary model based least-squares identification methods for Hammerstein outputerror systems, Syst. Control Lett. 56(5) (2007), pp. 373-380.
11. F. Ding, P.X. Liu, and G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal Process. 89(10) (2009), pp. 1883-1890.
12. F. Ding, L. Qiu, and T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discretetime systems, Automatica 45(2) (2009), pp. 324-332.
13. J. Ding, L.L. Han, and X.M. Chen, Time series AR modeling with missing observations based on the polynomial transformation, Math. Comput. Model. 51(5-6) (2010), pp. 527-536.
14. F. Ding, G. Liu, and X.P. Liu, Parameter estimation with scarce measurements, Automatica 47(8) (2011), pp. 1646-1655.
15. F. Ding, P.X. Liu, and G. Liu, Identification methods for Hammerstein nonlinear systems, Digital Signal Process. 21(2) (2011), pp. 215-238.
16. 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. Automat. Control 56(11) (2011), pp. 2677-2683.
17. F. Ding,Y.J. Liu, and B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems, Proc. Inst. Mech. Eng. I: J. Syst. Control Eng. 226(1) (2012), pp. 43-55.
18. H. Fang, J.Wu, andY. Shi, Genetic adaptive state estimation with missing input/output data, Proc. Inst. Mech. Eng. I, J. Syst. Control Eng. 224(5) (2010), pp. 611-617.
19. G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ, 1984.
20. Y. Gu and F. Ding, Auxiliary model based least squares identification method for a state space model with a unit time-delay, Appl. Math. Model. (2012), doi:10.1016/j.apm.2012.01.039.
21. J.H. Li and F. Ding, Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique, Comput. Math. Appl. 62(11) (2011), pp. 4170-4177
22. J.H. Li, F. Ding, and G.W.Yang, Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems, Math. Comput. Model. 55(3-4) (2012), pp. 442-450.
23. 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, Appl. Math. Comput. 215(4) (2009), pp. 1477-1483.
24. 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. Inst. Mech. Eng. I: J. Syst. Control Eng. 223(4) (2009), pp. 445-454.
25. Y.J. Liu, J. Sheng, and R.F. Ding, Convergence of stochastic gradient algorithm for multivariable ARX-like systems, Comput. Math. Appl. 59(8) (2010), pp. 2615-2627.
26. L. Ljung, System Identification: Theory for the User, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1999.
27. Y. Shi and H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment, Int. J. Control 83(3) (2010), pp. 538-551.
28. Y. Shi and B.Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains, IEEE Trans. Automat. Control 54(7) (2009), pp. 1668-1674.
29. Y. Shi, H. Fang, and M.Yan, Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs, Int. J. Robust Nonlinear Control, Special Issue on Control with Limited Information (Part II) 19(18) (2009), pp. 1976-1992.
30. D.Q.Wang, Least squares-based recursive and iterative estimation for output error moving average (OEMA) systems using data filtering, IET Control Theory Appl. 5(14) (2011), pp. 1648-1657.
31. D.Q. Wang and F. Ding, Input-output data filtering based recursive least squares identification for CARARMA systems, Digital Signal Process. 20(4) (2010), pp. 991-999.
32. D.Q.Wang and F. Ding, Least squares based and gradient based iterative identification forWiener nonlinear systems, Signal Process. 91(5) (2011), pp. 1182-1189.
33. L.Y. Wang, L. Xie, and X.F. Wang, The residual based interactive stochastic gradient algorithms for controlled moving average models, Appl. Math. Comput. 211(2) (2009), pp. 442-449.
34. D.Q. Wang, G.W. Yang, and R.F. Ding, Gradient-based iterative parameter estimation for Box-Jenkins systems, Comput. Math. Appl. 60(5) (2010), pp. 1200-1208.
35. 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, Math. Comput. Model. 52(1-2) (2010), pp. 309-317.
36. D.Q.Wang,Y.Y. Chu, and F. Ding, Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA, systems, Comput. Math. Appl. 59(9) (2010), pp. 3092-3098.
37. W. Wang, J.H. Li, and R.F. Ding, Maximum likelihood identification algorithm for controlled autoregressive autoregressive models, Int. J. Comput. Math. 88(16) (2011), pp. 3458-3467.
38. W. Wang, F. Ding, and J.Y. Dai, Maximum likelihood least squares identification for systems with autoregressive moving average noise, Appl. Math. Model. 36(5) (2012), pp. 1842-1853.
39. 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, Math. Comput. Model. 52(5-6) (2010), pp. 918-924.
40. Y.S. Xiao, Y. Zhang, J. Ding, and J.Y. Dai, The residual based interactive least squares algorithms and simulation studies, Comput. Math. Appl. 58(6) (2009), pp. 1190-1197.
41. L. Xie,Y.J. Liu et al., Modelling and identification for non-uniformly periodically sampled-data systems, IET Control Theory Appl. 4(5) (2010), pp. 784-794.
42. M. Yan and Y. Shi, Robust discrete-time sliding mode control for uncertain systems with time-varying state delay, IET Control Theory Appl. 2(8) (2008), pp. 662-674.
43. B.Yu,Y. Shi, and H.N. Huang, l2 - l∞ filtering for multirate systems based on lifted models, Circuits Systems Signal Process. 27(5) (2008), pp. 699-711.
44. Y. Zhang, Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods, Math. Comput. Model. 53(9-10) (2011), pp. 1810-1819.
45. Y. Zhang and G.M. Cui, Bias compensation methods for stochastic systems with colored noise, Appl. Math. Model. 35(4) (2011), pp. 1709-1716.
46. J.B. Zhang, F. Ding, and Y. Shi, Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems Control Lett. 58(1) (2009), pp. 69-75.
47. Z.N. Zhang, F. Ding, and X.G. Liu, Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems, Comput. Math. Appl. 61(3) (2011), pp. 672-682.
48. B. Zhou, J. Lam, and G.R. Duan, Gradient-based maximal convergence rate iterative method for solving linear matrix equations, Int. J. Comput. Math. 87(3) (2010), pp. 515-527.
49. L.F. Zhuang, F. Pan, and F. Ding, Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models, Appl. Math. Model. 36(8) (2012), pp. 3454-3463.