Least squares algorithm for an input nonlinear system with a dynamic subspace state space model

Nonlinear Dynamics

Volumn 75, Issue 1-2, 2014, Pages 49-61

  Wang, Dongqing ^a   Ding, Feng ^b   Ximei, Liu ^b  

^a QINGDAO UNIVERSITY   (China)

^b QINGDAO UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Hammerstein model; Hierarchical identification principle; Least squares; State space models

Indexed keywords

HAMMERSTEIN MODEL; HIERARCHICAL IDENTIFICATION PRINCIPLE; IDENTIFICATION MODEL; ITERATIVE LEAST SQUARES; LEAST SQUARE; LEAST SQUARES ALGORITHM; LEAST SQUARES METHODS; STATE - SPACE MODELS;

ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR SYSTEMS; STATE SPACE METHODS;

LEAST SQUARES APPROXIMATIONS;

EID: 84891556804     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-1048-8     Document Type: Article

References (66)

1. Ding, F.: System Identification - New Theory and Methods. Science Press, Beijing (2013)
2. Rashid, M.T.; Frasca, M.; Ali, A.A.; Ali, R.S.; Fortuna, L.; Xibilia, M.G.: Nonlinear model identification for Artemia population motion. Nonlinear Dyn. 69(4), 2237-2243 (2012)
3. Farjoud, A.; Ahmadian, M.; Craft, M.; Burke, W.: Nonlinear modeling and experimental characterization of hydraulic dampers: effects of shim stack and orifice parameters on damper performance. Nonlinear Dyn. 67(2), 1437-1456 (2012)
4. Gaite, J.: Nonlinear analysis of spacecraft thermal models. Nonlinear Dyn. 65(3), 283-300 (2011)
5. Shams, S.; Sadr, M.H.; Haddadpour, H.: An efficient method for nonlinear aeroelasticity of slender wings. Nonlinear Dyn. 67(1), 659-681 (2012)
6. Ding, F.; Liu, X.G.; Chu, J.: Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7(2), 176-184 (2013)
7. Smith, J.G.; Kamat, S.; Madhavan, K.P.: Modeling of pH process using wavenet based Hammerstein. J. Process Control 17(6), 551-561 (2007)
8. van der Veen, G.J.; van Wingerden, J.W.; Fleming, P.A.; Scholbrock, A.K.; Verhaegen, M.: Global data-driven modeling of wind turbines in the presence of turbulence. Control Eng. Pract. 21(4), 441-454 (2013)
9. Moon, J.; Kim, B.: Enhanced Hammerstein behavioral model for broadband wireless transmitters. IEEE Trans. Microw. Theory Tech. 59(4), 924-933 (2011)
10. Le, F.; Markovsky, I.; Freeman, C.T.; Rogers, E.: Recursive identification of Hammerstein systems with application to electrically stimulated muscle. Control Eng. Pract. 20(4), 386-396 (2012)
11. Wang, J.; Sano, A.; Chen, T.; Huang, B.: Identification of Hammerstein systems without explicit parameterization of nonlinearity. Int. J. Control 82(5), 937-952 (2009)
12. Liu, Y.; Bai, E.W.: Iterative identification of Hammerstein systems. Automatica 43(2), 346-354 (2007)
13. Li, J.H.: Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91-96 (2013)
14. Ding, F.; Chen, T.: Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479-1489 (2005)
15. Ding, F.; Shi, Y.; Chen, T.: Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dyn. 45(1-2), 31-43 (2006)
16. Ding, F.; Shi, Y.; Chen, T.: Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 56(5), 373-380 (2007)
17. Vanbeylen, L.; Pintelon, R.; Schoukens, J.: Blind maximum likelihood identification of Hammerstein systems. Automatica 44(12), 3139-3146 (2008)
18. Wang, J.; Sano, A.; Shook, D.; Chen, T.; Huang, B.: A blind approach to closed-loop identification of Hammerstein systems. Int. J. Control 80(2), 302-313 (2007)
19. Vörös, J.: Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Trans. Autom. Control 48(12), 2203-2206 (2003)
20. Vörös, J.: Identification of nonlinear cascade systems with time-varying backlash. J. Electr. Eng. 62(2), 87-92 (2011)
21. Wang, D.Q.; Chu, Y.Y.; Ding, F.: Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems. Comput. Math. Appl. 59(9), 3092-3098 (2010)
22. Wang, D.Q.; Chu, Y.Y.; Yang, G.W.; Ding, F.: Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems. Math. Comput. Model. 52(1-2), 309-317 (2010)
23. Chen, J.; Lv, L.X.; Ding, R.F.: Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity. Appl. Math. Lett. 26(1), 124-129 (2013)
24. Li, J.H.; Ding, F.: Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique. Comput. Math. Appl. 62(11), 4170-4177 (2011)
25. Li, J.H.; Ding, F.; Yang, G.W.: Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3-4), 442-450 (2012)
26. Wang, W.; Ding, F.; Dai, J.Y.: Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 36(5), 1842-1853 (2012)
27. Ding, F.; Liu, X.P.; Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215-238 (2011)
28. Bai, E.W.: An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3), 333-338 (1998)
29. Wang, D.Q.; Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182-1189 (2011)
30. Ding, F.; Gu, Y.: Performance analysis of the auxiliary model based least squares identification algorithm for one-step state delay systems. Int. J. Comput. Math. 89(15), 2019-2028 (2012)
31. Ding, F.; Gu, Y.: Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay. Circuits Syst. Signal Process. 32(2), 585-599 (2013)
32. Zhang, Y.: Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 53(9-10), 1810-1819 (2011)
33. Wang, D.Q.; Ding, F.: Hierarchical least squares estimation algorithm for Hammerstein-Wiener systems. IEEE Signal Process. Lett. 19(12), 825-828 (2012)
34. Ding, F.: Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694-1704 (2013)
35. Ding, F.; Chen, T.: Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50(3), 397-402 (2005)
36. Ding, F.; Chen, T.: Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41(2), 315-325 (2005)
37. Dehghan, M.; Hajarian, M.: An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Appl. Math. Model. 34(3), 639-654 (2010)
38. Dehghan, M.; Hajarian, M.: Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 35(7), 3285-3300 (2011)
39. Dehghan, M.; Hajarian, M.: The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations. Rocky Mt. J. Math. 40(3), 825-848 (2010)
40. Dehghan, M.; Hajarian, M.: On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations. Linear Multilinear Algebra 59(11), 1281-1309 (2011)
41. Dehghan, M.; Hajarian, M.: The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB+CYTD=E. Math. Methods Appl. Sci. 34(13), 61562-1579 (2011)
42. Dehghan, M.; Hajarian, M.: Solving the generalized Sylvester matrix equation $\sum-{i=1}^{p} A-{i}XB-{i}+\sum-{j=1}^{q}C-{j}YD-{j} = E$ over reflexive and anti-reflexive matrices. Int. J. Control. Autom. Syst. 9(1), 118-124 (2011)
43. Dehghan, M.; Hajarian, M.: Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations. Appl. Math. Lett. 24(4), 444-449 (2011)
44. 2. Bull. Iran. Math. Soc. 37(3), 269-279 (2011)
45. Dehghan, M.; Hajarian, M.: SSHI methods for solving general linear matrix equations. Eng. Comput. 28(8), 1028-1043 (2012)
46. Dehghan, M.; Hajarian, M.: The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices. Int. J. Syst. Sci. 43(8), 1580-1590 (2012)
47. Hashemi, B.; Dehghan, M.: Efficient computation of enclosures for the exact solvents of a quadratic matrix equation. Electron. J. Linear Algebra 20, 519-536 (2010)
48. Wang, D.Q.: Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648-1657 (2011)
49. Ding, F.; Liu, G.; Liu, X.P.: Parameter estimation with scarce measurements. Automatica 47(8), 1646-1655 (2011)
50. Ding, F.; Chen, T.: Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(6), 1179-1187 (2005)
51. Goodwin, G.C.; Sin, K.S.: Adaptive Filtering Prediction and Control. Prentice Hall, Englewood Cliffs (1984)
52. Shi, Y.; Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668-1674 (2009)
53. Shi, Y.; Yu, B.: Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754-760 (2011)
54. Ding, F.; Qiu, L.; Chen, T.: Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2), 324-332 (2009)
55. Liu, Y.J.; Sheng, J.; Ding, R.F.: Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615-2627 (2010)
56. Ding, F.; Liu, Y.J.; Bao, B.: Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng.; Part I, J. Syst. Control Eng. 226(1), 43-55 (2012)
57. Ding, F.: Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68-79 (2013)
58. Ding, F.: Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798-4808 (2013)
59. Ding, F.: Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235-1242 (2013)
60. Ding, F.; Chen, T.: Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1-14 (2007)
61. Liu, Y.J.; Xiao, Y.S.; Zhao, X.L.: Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477-1483 (2009)
62. Ding, F.: Several multi-innovation identification methods. Digit. Signal Process. 20(4), 1027-1039 (2010)
63. Ding, F.; Liu, X.P.; Liu, G.: Multi-innovation least squares identification for linear and pseudo-linear regression models. IEEE Trans. Syst. Man Cybern.; Part B, Cybern. 40(3), 767-778 (2010)
64. Hu, P.P.; Ding, F.: Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle. Nonlinear Dyn. 73(1-2), 583-592 (2013)
65. Han, H.Q.; Xie, L.; Ding, F.; Liu, X.: Hierarchical least squares based iterative identification for multivariable systems with moving average noises. Math. Comput. Model. 51(9-10), 1213-1220 (2010)
66. Zhang, Z.N.; Ding, F.; Liu, X.G.: Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 61(3), 672-682 (2011)