Rational basis functions for robust identification from frequency and time-domain measurements

Automatica

Volumn 34, Issue 9, 1998, Pages 1101-1117

  Akçay, Hüseyin ^a   Ninness, Brett ^b  

^a BOGAZICI UNIVERSITY   (Turkey)

^b UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Error analysis; Estimation; Identification; Robustness; Worst case analysis

Indexed keywords

ERROR ANALYSIS; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; POLES AND ZEROS; ROBUSTNESS (CONTROL SYSTEMS); TIME DOMAIN ANALYSIS;

RATIONAL BASIS FUNCTIONS;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0032166168     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(98)00052-1     Document Type: Article

References (70)

1. Achieser, N. I. (1992). Theory of Approximation. Dover Publications, New York, (Transl. C. J. Hyman).
2. ∞ with nonuniformly spaced frequency response data. In Proc. 36th IEEE Conf. Dec. Control, San Diego, CA, Math. Control Signals Systems, to appear.
3. ∞ with nonuniformly spaced frequency response data. In Proc. 36th IEEE Conf. Dec. Control, San Diego, CA, Math. Control Signals Systems, to appear.
4. ∞: continuous-time case. IEEE Trans. Automat. Control, 38, 289-294.
5. ∞ with nonuniformly spaced frequency response measurements. Int. J. Robust Nonlinear Control, 4, 613-629.
6. Akçay, H., S. M. Islam and B. Ninness (1997). Identification of power transformer models from frequncy response data: a case study. Signal Processing, to appear.
7. Barrodale, I. and C. Phillips (1975). Algorithm 495, solution of an overdetermined system of linear equations in the Chebyshev norm [f4]. ACM Trans. Math. Software, 1, 264-270.
8. Bodin, P. and B. Wahlberg (1994). Thresholding in high order transfer function estimation. In Proc. 33rd IEEE Conf. Dec. Control, Lake Buena Vista, FL, pp. 3400-3405.
9. 2. Technical report, Computer and Automation Institute, Hungarian Academy of Sciences.
10. ∞ identification using partial sum operators in disc algebra basis. In Proc. Amer. Control Conf., pp. 1981-1985.
11. Borwein, P. and T. Erdelyi (1996). Sharp extensions of Bernstein's inequality to rational spaces. Mathematika, 43, 413-423.
12. Caines, P. (1996). Linear Stochastic Systems. Wiley, New York.
13. ∞: validation of a priori information, essentially optimal algorithms and error bounds. IEEE Trans. Automat. Control, 40, 1260-1265.
14. Dahleh, M. and M. Khammash. Controller design for plants with structured uncertainty. Automatica, 29, 37-56.
15. Dahleh, M. A., T. Theodosopoulos and J. N. Tsitsiklis (1993). The sample complexity of worst-case identification of FIR linear systems. Systems Control Lett. 20, 157-166.
16. den Brinker, A. C. (1996). Optimality conditions for a specific class of truncated Kautz series. IEEE Trans. Circuits Systems - Part II, 43, 597-600.
17. Dewilde, P. and H. Dym (1981). Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences. IEEE Trans. Information Theory, 27, 446-461.
18. p Spaces. Academic Press, New York and London.
19. 1 identification using mixed parametric-nonparametric models. In Proc. 32nd IEEE Conf. Dec. Control, San Antonio, Texas, pp. 545-550.
20. Fu, Y. and G. A. Dumont (1993). On determination of Laguerre filter pole through step or impulse response data. In Proc. 12th IFAC World Congress, Sydney, Australia, Vol. 5, pp. 303-307.
21. ∞ identification and model quality evaluation. IEEE Trans. Automat. Control, 42, 188-199.
22. ∞ and model validation. IEEE Trans. Automat. Control, 39, 1657-1661.
23. ∞. Automatica, 28, 229-242.
24. ∞ with error bounds. IEEE Trans. Automat. Control, 37, 953-963.
25. ∞ using Pick's interpolation. Systems Control Lett., 20, 263-272.
26. Harrison, K. J., J. R. Partington and J. A. Ward (1997). Complexity of identification of discrete-time linear systems with rational transfer functions. Preprint.
27. Harrison, K. J. and J. A. Ward (1996). Fractional covers for convolution products. Result. Math., 30, 67-78.
28. Harrison, K. J., J. A. Ward and D. K. Gamble (1996). Sample complexity of worst-case identification. Systems Control Lett., 27, 255-260.
29. Hayman, W. K. and T. J. Lyons (1990). Bases for positive continuous functions. J. London Math. Soc., 42, 292-308.
30. ∞. IEEE Trans. Automat. Control, 36, 1163-1176.
31. Heuberger, P. S. C., P. M. J. Van den Hof and O. H. Bosgra (1995). A generalized orthonormal basis for linear dynamical systems. IEEE Trans. Automat. Control, 40, 451-465.
32. 1 identification with bounded noise. Int. J. Adaptive Control Signal Processing, 9, 87-96.
33. Kosut, R. L., M. K. Lau and S. P. Boyd (1992). Set membership identification of systems with parametric and non-parametric uncertainty. IEEE Trans. Automat. Control, 37, 929-941.
34. Kung, S. Y. (1978). A new identification and model reduction algorithm via singular value decomposition. In Proc. 12th Asilomar Conference on Circuits, Systems and Computers, Pacific Grove, CA, pp. 705-714.
35. Ljung, L. (1987). System Identification: Theory for the User. Prentice-Hall, Englewood Cliffs, NJ.
36. Mäkilä, P. (1990). Laguerre series approximation of infinite dimensional systems. Automatica, 26, 985-995.
37. Mäkilä, P. M. (1990) Robust identification and Galois sequences. Int. J. Control, 54, 1189-1200.
38. Mäkilä, P. M. and J. R. Partington (1992). Robust identification of strongly stabilizable systems. IEEE Trans. Automat. Control, 37, 1709-1716.
39. Mäkilä, P. M., J. R. Partington and T. Gustafsson (1995). Worst-case control-relevant identification. Automatica, 31, 1799-1820.
40. McKelvey, T., H. Akçay and L. Ljung (1996). Subspace-based multivariable system identification from frequency response data. IEEE Trans. Automat. Control, 41, 960-979.
41. Ninness, B. and G. Goodwin (1995). Estimation of model quality. Automatica, 31, 32-74.
42. Ninness, B. and F. Gustafsson (1997). A unifying construction of orthonormal bases for system identification. IEEE Trans. Automat. Control, 42, 515-521.
43. Ninness, B. and H. Hjalmarsson (1997). Generalised Fourier and Toeplitz results for rational orthonormal bases. Technical Report EE9740, Dept. Elec. and Comp. Eng., Univ. Newcastle, Australia. SIAM J. Control Optim., (submitted).
44. Ninness, B., H. Hjalmarsson and F. Gustafsson (1997). The Fundamental role of orthonormal bases in system identification. Technical Report EE9739, Dept. Elec. and Comp. Eng., Univ. Newcastle, Australia. IEEE Trans. Automat. Control. (submitted).
45. Oliveira e Silva, T. (1995). On the determination of the optimal pole position of Laguerre filters. IEEE Trans. Signal Process., 49, 2079-2087.
46. Oliveira e Silva, T. (1996). N-width result for the generalized orthonormal basis function model. In Proc. 13th IFAC World Congr., Vol. I, pp. 375-380, San Fransisco, CA.
47. ∞. Int. J. Control, 54, 1281-1290.
48. ∞. J. Math. Anal. Appl., 166, 428-441.
49. ∞ with unequally spaced function measurements. Int. J. Control, 58, 21-31.
50. Partington, J. R. (1994). Interpolation in normed spaces from the values of linear functionals. Bull. London Math. Soc., 26, 165-170.
51. 2: linear and non-linear algorithms. Systems Control Lett., 22, 93-98.
52. Partington, J. R. (1996). Recovery of functions by interpolation and sampling. J. Math. Anal. Appl., 198, 301-309.
53. Partington, J. R. and P. M. Mäkilä (1995). Worst-case analysis of the least-squares method and related identification methods. Systems Control Lett., 24, 193-200.
54. Pinkus, A. (1985). n-Widths in Approximation Theory. Springer, Berlin.
55. Poolla, K. and A. Tikku (1994). On the time complexity of worst-case system identification. IEEE Trans. Automat. Control, 39, 944-950.
56. Rudin, W. (1987). Real and Complex Analysis. 3rd edn. McGraw-Hill, New York.
57. ∞ norm. Preprint.
58. Schipp, F., L. Gianone and Z. Szabo (1996). Identification in generalized orthonormal basis - a frequency domain approach. In Proc. 13th IFAC World Congress, San Fransisco, pp. 387-392.
59. Söderström, T. and P. Stoica. (1989). System Identification. Prentice Hall Int., Hemel Hempstead, Hertfordshire.
60. Somorjai, G. (1977). On discrete linear operators in the function space A. In Proc. Constructive Function Theory, Blagoevgrad, Sofia, 1980. H. Bulgarian Acad. Sci. pp. 489-500.
61. ∞ using generalized orthonormal basis. IEEE Trans. Automat. Control, (to appear).
62. Tse, T., M. Dahleh and J. Tsitsiklis (1993). Optimal asymptotic identification under bounded disturbances. IEEE Trans. Automat. Control, 38, 1176-1190.
63. Van den Hof, P. M. J., P. S. C. Heuberger and J. Bokor (1995). System identification with generalized orthonormal basis functions. Automatica, 31, 1821-1834.
64. Wahlberg, B. (1991). System identification using Laguerre models. IEEE Trans. Automat. Control, 36, 551-562.
65. Wahlberg, B. (1994). System identification using Kautz models. IEEE Trans. Automat. Control, AC-39, 1276-1282.
66. Wahlberg, B. and L. Ljung (1992). Hard frequency-domain model error bounds from least-squares like identification techniques. IEEE Trans. Automat. Control, AC-37, 900-912.
67. Ward, N. F. D. and J. R. Partington (1995). Rational wavelet decomposition of transfer functions in Hardy-Sobolev classes. Math. Control Signals Systems, 8, 257-278.
68. Ward, N. F. D. and J. R. Partington (1996). Robust identification in the disk algebra using rational wavelets and orthonormal basis functions. Int. J. Control, 64, 409-423.
69. Zimmermann, S. and G. A. Williamson (1994). Selecting pole locations for system identifiers with fixed poles. In Proc. 10th IFAC Symp. Systems Identif., Copenhagen, Denmark, Vol. 3, pp. 519-524.
70. Zygmund, A. (1959). Trigonometric Series. Cambridge University Press, Cambridge.