A geometric approach to variance analysis in system identification

IEEE Transactions on Automatic Control

Volumn 56, Issue 5, 2011, Pages 983-997

  Hjalmarsson, Håkan ^a   Mårtensson, Jonas ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Asymptotic covariance; model accuracy; stochastic systems; system identification

Indexed keywords

ASYMPTOTIC COVARIANCE; DATA LENGTH; DYNAMIC SYSTEMS; EXPERIMENTAL CONDITIONS; GEOMETRIC APPROACHES; MODEL ACCURACY; ORTHOGONAL PROJECTION; QUANTIFYING THE MODELS; SMOOTH FUNCTIONS; SYSTEM IDENTIFICATION; SYSTEM IDENTIFICATIONS; SYSTEM PROPERTY; VARIANCE ANALYSIS;

ORTHOGONAL FUNCTIONS; STRUCTURAL ANALYSIS;

STOCHASTIC MODELS;

EID: 79955911807     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2076213     Document Type: Article

References (68)

1. J. Antoni and J. Schoukens, "A comprehensive study of the bias and variance of frequency-response-function measurements: Optimal window selection and overlapping strategies," Automatica, vol. 43, no. 10, pp. 1723-1736, 2007. (Pubitemid 47374626)
2. X. Bombois, B. Anderson, and M. Gevers, "Mapping parametric confidence ellipsoids to Nyquist plane for linearly parametrized transfer functions," in Model Identification and Adaptative Control, G. Goodwin, Ed. New York: Springer Verlag, 2000, pp. 53-71.
3. M. Campi and E. Weyer, "Finite sample properties of system identification methods," IEEE Trans. Autom. Contr., vol. 47, no. 8, pp. 1329-1334, Aug. 2002. (Pubitemid 34959768)
4. S. Douma and P. V. den Hof, "Relations between uncertainty structures in identification for robust control," Automatica, vol. 41, no. 3, pp. 439-457, 2005. (Pubitemid 40183242)
5. M. Gevers, L. Ljung, and P. Van den Hof, "Asymptotic variance expressions for closed-loop identification," Automatica, vol. 37, no. 5, pp. 781-786, 2001. (Pubitemid 32264807)
6. R. Hakvoort and P. Van den Hof, "Identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors," IEEE Trans. Autom. Contr., vol. 42, no. 11, pp. 1516-1528, Nov. 1997. (Pubitemid 127760297)
7. R. Hildebrand and M. Gevers, "Quantification of the variance of estimated transfer functions in the presence of undermodelling," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, 2003, pp. 1850-1855.
8. H. Hjalmarsson, "From experiment design to closed loop control," Automatica, vol. 41, no. 3, pp. 393-438, Mar. 2005. (Pubitemid 40183241)
9. L. Ljung, "Perspectives on system identification," in Proc. 17th IFAC World Congress, Seoul, Korea, Jul. 2008, pp. 7172-7184.
10. L. Ljung and L. Guo, "The role of model validation for assessing the size of the unmodeled dynamics," IEEE Trans. Autom. Cotntr., vol. 42, no. 9, pp. 1230-1239, 1997. (Pubitemid 127760892)
11. M. Milanese and C. Novara, "Model quality in nonlinear SM identification," in Proc. 42nd IEEE Conf. Decision Control, Maui, HI, Dec. 2003, pp. 6021-6026.
12. M. Milanese and A. Vicino, "Optimal estimation theory for dynamic systems with set membership uncertainty: An overview," Automatica, vol. 27, no. 6, pp. 997-1009, 1991.
13. M. Milanese and A. Vicino, "H∞ set membership identification: A survey," Automatica, vol. 41, no. 12, pp. 2019-2032, 2005.
14. B. Ninness, "On the CRLB for combined model and model order estimation of stationary stochastic processes," IEEE Signal Process. Lett., vol. 11, pp. 293-296, Feb. 2004.
15. B. Ninness and G. Goodwin, "Estimation of model quality," Automatica, vol. 31, no. 12, pp. 32-74, 1995.
16. B. Ninness and S. Henriksen, "System identification via a computational Bayesian approach," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, 2003, pp. 785-790.
17. B. Ninness and H. Hjalmarsson, "On the frequency domain accuracy of closed-loop estimates," Automatica, vol. 41, no. 7, pp. 1109-1122, 2005. (Pubitemid 40644851)
18. R. Pintelon, P. Guillaume, and J. Schoukens, "Uncertainty calculation in (operational) modal analysis," Mech. Syst. Signal Process., vol. 21, no. 6, pp. 2359-2373, 2007. (Pubitemid 46829747)
19. R. Pintelon, J. Schoukens, and Y. Rolain, "Uncertainty of transfer function modelling using prior estimated noise models," Automatica, vol. 39, no. 10, pp. 1721-1733, 2003.
20. W. Reinelt, A. Garulli, and L. Ljung, "Comparing different approaches to model error modeling in robust identification," Automatica, vol. 38, no. 5, pp. 787-803, May 2002. (Pubitemid 34201120)
21. B. Wahlberg and L. Ljung, "Hard frequency-domain model error bounds from least-squares like identification techniques," IEEE Trans. Autom. Contr., vol. 37, no. 7, pp. 900-912, Jul. 1992.
22. L. Ljung, System Identification: Theory for the User, 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1999.
23. V. Fedorov, Theory of Optimal Experiments, ser. Probability and Mathematical Statistics. New York: Academic, 1972, vol. 12.
24. G. Goodwin and R. Payne, Dynamic System Identification: Experiment Design and Data Analysis, ser. Mathematics in Science and Engineering. New York: Academic, 1977, vol. 136.
25. R. Mehra, "Optimal input signals for parameter estimation in dynamic systems-Survey and new results," IEEE Trans. Autom. Contr., vol. 19, no. 12, pp. 753-768, Dec. 1974.
26. M. Zarrop, Optimal Experiment Design for Dynamic System Identification. Berlin, Germany: Springer Verlag, 1979, Lecture Notes in Control and Information Sciences. Sci. 21.
27. L. Ljung, "Asymptotic variance expressions for identified black-box transfer function models," IEEE Trans. Autom. Contr., vol. 30, no. 9, pp. 834-844, Sep. 1985. (Pubitemid 16494285)
28. U. Forssell and L. Ljung, "Some results on optimal experiment design," Automatica, vol. 36, no. 5, pp. 749-756, May 2000. (Pubitemid 30578687)
29. M. Gevers and L. Ljung, "Optimal experiment designs with respect to the intended model application," Automatica, vol. 22, pp. 543-554, 1986. (Pubitemid 17465673)
30. H. Hjalmarsson, M. Gevers, and F. D. Bruyne, "For model-based control design, closed-loop identification gives better performance," Automatica, vol. 32, no. 12, pp. 1659-1673, 1996. (Pubitemid 126647291)
31. Z. Yuan and L. Ljung, "Unprejudiced optimal open loop input design for identification of transfer functions," Automatica, vol. 21, no. 6, pp. 697-708, 1985. (Pubitemid 16488085)
32. G. Belforte and P. Gay, "Optimal experiment design for regression polynomial models identification," Int. J. Contr., vol. 75, no. 15, pp. 1178-1189, Oct. 2002. (Pubitemid 35459891)
33. G. Franceschini and S. Macchietto, "Model-based design of experiments for parameter precision: State of the art," Chem. Eng. Sci., vol. 63, no. 19, pp. 4846-4872, 2008.
34. C. Jauberthie, L. Denis-Vidal, P. Coton, and G. Joly-Blanchard, "An optimal input design procedure," Automatica, vol. 42, no. 5, pp. 881-884, 2006.
35. L. Pronzato, "Adaptive optimization and D-optimum experimental design," Ann. Statist., vol. 28, no. 6, pp. 1743-1761, 2000. (Pubitemid 33274482)
36. L. Pronzato, "Optimal experimental design and some related control problems," Automatica, vol. 44, no. 2, pp. 303-325, 2008.
37. C. R. Rojas, J. S.Welsh, G. C. Goodwin, and A. Feuer, "Robust optimal experiment design for system identification," Automatica, vol. 43, no. 6, pp. 993-1008, 2007. (Pubitemid 46653813)
38. Y. Zhu,Multivariable System Identification for Process Control. Oxford, U.K.: Elsevier Science, 2001.
39. Y. Zhu, "System identification for process control: recent experience and outlook," Int. J. Modelling, Identification Contr., vol. 6, no. 2, pp. 89-103, 2009.
40. P. Celaya, R. Tkatch, Y. Zhu, and R. Patwardhan, "Closed-loop identification at the Hovensa refinery," presented at the NPRA Plant Autom. Decision Support Conf., San Antonio, TX, 2004.
41. P. Zehna, "Invariance of maximum likelihood estimators," Ann. Math. Statist., vol. 37, no. 755, pp. 744-744, 1966.
42. H. Hjalmarsson, "System identification of complex and structured systems," Eur. J. Control/Plenary Address Eur. Contr. Conf., vol. 15, no. 3-4, pp. 275-310, May-Aug. 2009.
43. P. Stoica and T. Marzetta, "Parameter estimation problems with singular information matrices," IEEE Trans. Signal Process., vol. 49, pp. 87-90, Jan. 2001. (Pubitemid 32137126)
44. G. Box and G. Jenkins, Time Series Analysis, Forecasting and Control. Oakland, CA: Holden-Day, 1976.
45. I. Gustavsson, L. Ljung, and T. Söderström, "Identification of processes in closed-loop-Identifiability and accuracy aspects," Automatica, vol. 13, no. 1, pp. 59-75, 1977. (Pubitemid 8545610)
46. M. Gevers, L. Miskovic, D. Bonvin, and A. Karimi, "Identification of multi-input systems: variance analysis and input design issues," Automatica, vol. 42, no. 4, pp. 559-572, 2006. (Pubitemid 43267650)
47. M. Gevers, A. Bazanella, X. Bombois, and L. Miskovic, "Identification and the information matrix: How to get just sufficiently rich?," IEEE Trans. Autom. Contr., vol. 54, no. 12, pp. 2828-2840, Dec. 2009.
48. B. Ninness and S. Gibson, "Quantifying the accuracy of Hammerstein model estimation," Automatica, vol. 38, no. 12, pp. 2037-2051, 2002. (Pubitemid 35276205)
49. M. Campi, S. Ooi, and E. Weyer, "Non-asymptotic quality assessment of generalised FIR models with periodic inputs," Automatica, vol. 40, no. 12, pp. 2029-2041, 2004.
50. M. Campi and E. Weyer, "Guaranteed non-asymptotic confidence regions in system identification," Automatica, vol. 41, no. 10, pp. 1751-1764, 2005. (Pubitemid 41119032)
51. S. Douma and P. Van den Hof, "Probabilistic model uncertainty bounding: An approach with finite-time perspectives," in Proc. 4th IFAC Symp. System Identification, Newcastle, Australia, Mar. 27-29, 2006, pp. 1021-1026.
52. S. Garatti, M. Campi, and S. Bittanti, "Assessing the quality of identified models through the asymptotic theory-When is the result reliable?," Automatica, vol. 40, no. 8, pp. 1319-1332, 2004.
53. B. Ninness and H. Hjalmarsson, "Variance error quantifications that are exact for finite model order," IEEE Trans. Autom. Contr., vol. 49, pp. 1275-1291, 2004.
54. L. Scharf and L. McWorter, "Geometry of the Cramer-Rao bound," Signal Process., vol. 31, no. 3, pp. 301-311, 1993. (Pubitemid 23639966)
55. E. Dilaveroglu, "Simple general expression for Cramér-Rao bound in presence of nuisance parameters," Electron. Lett., vol. 38, no. 25, pp. 1750-1751, 2002.
56. H. Hjalmarsson and J. Mårtensson, "A geometric approach to variance analysis in system identification: Theory and nonlinear systems," in Proc. 46th IEEE Conf. Decision Contr., New Orleans, LA, Dec. 2007, pp. 5092-5097. (Pubitemid 351277948)
57. A. Friedman, Foundations of Modern Analysis. New York: Dover, 1982.
58. J. Mårtensson and H. Hjalmarsson, "Variance analysis in SISO linear systems identification," IEEE Trans. Autom. Contr., 2011, provisionally accepted for publication.
59. J. Mårtensson and H. Hjalmarsson, "A geometric approach to variance analysis in system identification: Linear time-invariant systems," in 46th IEEE Conf. Decision Contr., Dec. 2007, pp. 4269-4274. (Pubitemid 351277815)
60. H. Hjalmarsson, "Aspects on incomplete modeling in system identification," Ph.D. dissertation, Linköping University, Sweden, Sweden, 1993.
61. K. Lindqvist and H. Hjalmarsson, "Identification of performance limitations in control," in Proc. Eur. Contr. Conf., Porto, Portugal, 2001, pp. 1446-1451.
62. J. Mårtensson and H. Hjalmarsson, "Variance error quantification for identified poles and zeros," Automatica, vol. 45, no. 11, pp. 2512-2525, Nov. 2009.
63. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
64. H. Hjalmarsson, J. Mårtensson, and B.Wahlberg, "On some robustness issues in input design," in Proc. 14th IFAC Symp. Syst. Identification, Mar. 2006, pp. 511-516.
65. J. Mårtensson and H. Hjalmarsson, "How to make bias and variance errors insensitive to system and model complexity in identification," IEEE Trans. Autom. Contr., vol. 56, no. 1, pp. 100-112, 2011.
66. J. Mårtensson, Geometric Analysis of Stochastic Model Errors in System Identification KTH, Stockholm, Sweden, 2007 [Online]. Available: http://www.ee.kth.se/∼jonas1/thesis.pdf
67. T. Söderström and P. Stoica, System Identification. : Prentice Hall International series in systems and control engineering, 1989.
68. B. Wahlberg, H. Hjalmarsson, and J. Mårtensson, "Variance results for identification of cascade systems," Automatica, vol. 45, no. 6, pp. 1443-1448, Jun. 2009.