Variance-error quantification for identified poles and zeros

Automatica

Volumn 45, Issue 11, 2009, Pages 2512-2525

  Mårtensson, Jonas ^a   Hjalmarsson, Håkan ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Accuracy of identification; Asymptotic variance expressions

Indexed keywords

ACCURACY OF IDENTIFICATION; ASYMPTOTIC VARIANCE; ASYMPTOTIC VARIANCE EXPRESSIONS; BLACK-BOX MODEL; BOX-JENKINS MODELS; DATA LENGTH; DISCRETE-TIME MODEL; ERROR QUANTIFICATION; FINITE LIMITS; LINEAR TIME INVARIANT SYSTEMS; MODEL ERRORS; MODEL ORDER; NOISE-INDUCED ERRORS; UNIT CIRCLES;

INVARIANCE; MODEL STRUCTURES; MULTIVARIABLE CONTROL SYSTEMS; POLES; POLES AND ZEROS; TIME VARYING CONTROL SYSTEMS;

ASYMPTOTIC ANALYSIS;

EID: 70349883931     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.08.001     Document Type: Article

References (33)

1. Agüero J., and Goodwin G. Choosing between open- and closed-loop experiments in linear system identification. IEEE Transactions on Automatic Control 52 8 (2007) 1475-1480
2. Bombois, X., Gevers, M., & Scorletti, G. (2005). Open-loop versus closed-loop identification of Box-Jenkins models: A new variance analysis. In 44th IEEE conference on decision and control and the European control conference 2005 (pp. 3117-3122)
3. Bombois X., Scorletti G., Gevers M., Van den Hof P., and Hildebrand R. Least costly identification experiment for control. Automatica 42 10 (2006) 1651-1662
4. Forssell U., and Ljung L. Closed-loop identification revisited. Automatica 35 7 (1999) 1215-1241
5. Gevers, M., Bazanella, A. S., Bombois, X., & Miskovic, L. (2009). Identification and the information matrix: How to get just sufficiently rich? IEEE Transactions on Automatic Control (in press). To appear December 2009
6. Gevers M., Ljung L., and Van den Hof P. Asymptotic variance expressions for closed-loop identification. Automatica 37 5 (2001) 781-786
7. Grenander U., and Szegö G. Toeplitz forms and their applications (1958), University of California Press, Berkley, CA
8. In: Heuberger P., Wahlberg B., and den Hof P.V. (Eds). Modeling and identification with rational orthogonal basis functions (2005), Springer Verlag
9. Hjalmarsson, H., & Lindqvist, K. (2002). Identification of performance limitations in control using ARX-models. In Proceedings of The 15th IFAC world congress
10. Hjalmarsson, H., & Mårtensson, J. (2007). A geometric approach to variance analysis in system identification: Theory and nonlinear systems. In Proceedings of the 46th IEEE conference on decision and control (pp. 5092-5097)
11. Hjalmarsson H., and Ninness B. Least-squares estimation of a class of frequency functions: A finite sample variance expression. Automatica 42 4 (2006) 589-600
12. Lindqvist, K. (2001). On experiment design in identification of smooth linear systems. Licentiate thesis. Royal Institute of Technology, Stockholm, Sweden
13. Ljung L. Asymptotic variance expressions for identified Black-Box transfer function models. IEEE Transactions Automatic Control 30 9 (1985) 834-844
14. Ljung L. System identification: Theory for the user. second ed. (1999), Prentice Hall
15. Mårtensson, J., & Hjalmarsson, H. (2003). Identification of performance limitations in control using general SISO-models. In Proceedings of the 13th IFAC symposium on system identification (pp. 519-524)
16. Mårtensson, J., & Hjalmarsson, H. (2005a). Closed loop identification of unstable poles and non-minimum phase zeros. In Proceedings of the 16th IFAC world congress on automatic control
17. Mårtensson, J., & Hjalmarsson, H. (2005b). Exact quantification of the variance of estimated zeros. In Proceedings of the 44th IEEE conference on decision and control and European control conference (pp. 4275-4280)
18. Mårtensson, J., & Hjalmarsson, H. (2007). A geometric approach to variance analysis in system identification: Linear time-invariant systems. In Proceedings of the 46th IEEE conference on decision and control (pp. 4269-4274)
19. Mårtensson, J., Jansson, H., & Hjalmarsson, H. (2005). Input design for identification of zeros. In Proceedings of the 16th IFAC world congress on automatic control
20. Ninness B., and Gustafsson F. A unifying construction of orthonormal bases for system identification. IEEE Transactions on Automatic Control 42 4 (1997) 515-521
21. Ninness B., and Hjalmarsson H. Variance error quantifications that are exact for finite model order. IEEE Transactions on Automatic Control 49 8 (2004) 1275-1291
22. Ninness B., and Hjalmarsson H. Analysis of the variability of joint input-output estimation methods. Automatica 41 7 (2005) 1123-1132
23. Ninness B., and Hjalmarsson H. On the frequency domain accuracy of closed-loop estimates. Automatica 41 7 (2005) 1109-1122
24. Ninness B., Hjalmarsson H., and Gustafsson F. Generalized Fourier and Toeplitz results for rational orthonormal bases. SIAM Journal on Control and Optimization 37 2 (1998) 429-460
25. Ninness, B., Hjalmarsson, H., & Gustafsson, F. (1999a). Asymptotic variance expressions for output error model structures. In 14th IFAC world congress, Vol. H (pp. 367-372)
26. Ninness B., Hjalmarsson H., and Gustafsson F. The fundamental role of general orthonormal bases in system identification. IEEE Transactions on Automatic Control 44 7 (1999) 1384-1406
27. Oppenheim A., and Schafer R. Discrete-time signal processing (1989), Prentice-Hall, Englewood Cliffs, NJ
28. Rudin W. Real and complex analysis. third ed. (1987), McGraw-Hill, Inc.
29. Skogestad S., and Postlethwaite I. Multivariable feedback control-Analysis and design (1996), John Wiley, Chichester
30. Söderström T., and Stoica P. System identification. Prentice Hall International series in systems and control engineering (1989)
31. Vuerinckx R., Pintelon R., Schoukens J., and Rolain Y. Obtaining accurate confidence regions for the estimated zeros and poles in system identification problems. IEEE Transactions on Automatic Control 46 4 (2001) 656-659
32. Xie L., and Ljung L. Asymptotic variance expressions for estimated frequency functions. IEEE Transactions on Automatic Control 46 12 (2001) 1887-1899
33. Xie L., and Ljung L. Variance expressions for spectra estimated using auto-regressions. Journal of Econometrics 118 1-2 (2004) 247-256