Set membership parameter estimation of fractional models based on bounded frequency domain data

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 4, 2010, Pages 927-938

  Malti, Rachid ^a   Raïssi, Tarek ^a   Thomassin, Magalie ^a   Khemane, Firas ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Bounded error; Complex interval analysis; Fractional differentiation; Fractional models; Frequency domain; Real interval analysis; Set membership; System identification; Uncertain data

Indexed keywords

CONSTRAINT SATISFACTION PROBLEMS; FREQUENCY ESTIMATION; UNCERTAINTY ANALYSIS;

BOUNDED ERRORS; COMPLEX INTERVAL; COMPLEX INTERVAL ANALYSE; FRACTIONAL DIFFERENTIATION; FRACTIONAL MODEL; FREQUENCY DOMAINS; INTERVAL ANALYSIS; REAL INTERVAL ANALYSE; REAL INTERVALS; SET-MEMBERSHIP; SYSTEM-IDENTIFICATION; UNCERTAIN DATAS;

FREQUENCY RESPONSE;

EID: 70350369911     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.05.005     Document Type: Article

References (35)

1. Milanese M., Norton J., Piet-Lahanier H., and Walter E. Bounding approaches to system identification (1996), Plenum, New York
2. Schweppe F. Recursive state estimation: unknown but bounded errors and system inputs. IEEE Trans Automat Contr 13 1 (1968) 22-28
3. Bertsekas I., and Rhodes D. Recursive state estimation for a set-membership description of uncertainty. IEEE Trans Automat Contr 16 2 (1971) 117-128
4. Durieu C., Walter E., and Polyak B. Multi-input multi-output ellipsoidal state bounding. J Opt Theory Appl 111 2 (2001) 273-303
5. Jaulin L., and Walter E. Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica 29 4 (1993) 1053-1064
6. Jaulin L., Kieffer M., Didrit O., and Walter E. Applied interval analysis (2001), Springer-Verlag, London
7. Samko S., Kilbas A., and Marichev O. Fractional integrals and derivatives: theory and applications (1993), Gordon and Breach Science
8. Oldham K., and Spanier J. The fractionnal calculus - theory and applications of differentiation and integration to arbitrary order (1974), Academic Press, New-York and London
9. The American Heritage (R). Dictionary of the English Language. Houghton Mifflin Company, Boston, 2000.
10. Matignon D. Stability properties for generalized fractional differential systems, ESAIM proceedings-Systèmes Différentiels Fractionnaires- Modèles, Méthodes et Applications 5.
11. Levy E. Complex curve fitting. IRE Trans Autom Control 4 (1959) 37-43
12. Sanathanan C., and Koerner J. Transfer function synthesis as a ratio of two complex polynomilas. IEEE Trans Autom Control AC-8 (1963) 56-58
13. ∞ transfer function curve fitting. Proc AIAA Guid Navig Control Conf (1991) 1739-1747
14. Hakvoort R. Frequency domain curve fitting with maximum amplitude criterion and guaranted stability, in: 2nd European Control Conf., Netherlands, 1993, pp. 252-257.
15. Pintelon R., Guillaume P., Rolain Y., Schoukens J., and Van Hamme H. Parametric identification of transfer functions in the frequency domain: a survey. IEEE Transactions on Automatic Control 39 11 (1994) 2245-2260
16. Mathieu B, Oustaloup A, Levron F. Transfer function parameter estimation by interpolation in the frequency domain, in: EEC'95, Rome, Italie, 1995.
17. Le Lay L. Identification fréquentielle et temporelle par modèle non entier, Ph.D. thesis, Université Bordeaux 1, Talence, France (1998).
18. Valério D, da Costa S. J., Advances in Fractional Calculus Theoretical Developments and Applications in Physics and Engineering, Springer, 2007, Ch. Identification of fractional models from frequency data, pp. 229-242.
19. Sunaga T. Theory of interval algebra and its application to numerical analysis. RAAG Memoirs 2 (1958) 29-46
20. Moore R. Interval analysis (1966), Prentice-Hall, Englewood Cliffs, NJ
21. Alefeld G., and Herzberger J. Introduction to interval computations (1983), Academic Press, New-York
22. Petkovic M.S., and Petkovic L.D. Complex interval arithmetic and its applications (1998), Wiley-VCH, Berlin
23. Henrici P. Circular arithmetic and the determination of polynomial zeros, Springer Lecture Notes 1971; 228: 86-92.
24. Klatte R., and Ullrich C. Complex sector arithmetic. Computing 24 2-3 (1980) 139-148
25. Rokne J., and Lancaster P. Complex interval arithmetic. ACM 14 (1971) 111-112
26. Kearfott R.B. Rigorous global search: continuous problems (1996), Kluwer Academic Publishers., Dordrecht, Netherlands
27. Nickel K. Arithmetic of complex sets. Computing 24 (1980) 97-105
28. Hansen E.R., and Walster G.W. Global optimization using interval analysis. second ed. (2004), Marcel Dekker, New-York, USA
29. Waltz DL. The psychology of computer vision, New-York, 1975, Ch. Generating semantic descriptions from drawing of scenes with shadows, pp. 19-91.
30. Davis E. Constraint propagation with interval labels. Artificial Intelligence 32 3 (1987) 281-331
31. Cleary J.C. Logical arithmetic. Future Computing Systems 2 2 (1987) 125-149
32. Ljung L. System identification- Theory for the user. second ed. (1999), Prentice-Hall, Upper Saddle River, NJ, USA
33. Antoni J, S.J., A comprehensive study of the bias and variance of frequency-response-function measurements: optimal window selection and overlapping strategies, Automatica Preprints.
34. Candau Y., Rai{dotless}̈ssi T., Ibos L., and Ramdani N. Complex interval arithmetic using polar form. Reliable Computing 12 1 (2006) 1-20
35. Malti R, Moreau X, Khemane F. Resonance of fractional transfer functions of the second kind, in: 3rd IFAC Workshop on Fractional Differentiation and its Applications, FDA'08, Ankara, Turkey, 2008.