An algebraic framework for linear identification

Michel Fliess; Hebertt Sira-Ramírez[1]

  • [1] Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique

ESAIM: Control, Optimisation and Calculus of Variations (2003)

  • Volume: 9, page 151-168
  • ISSN: 1292-8119

Abstract

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A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

How to cite

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Fliess, Michel, and Sira-Ramírez, Hebertt. "An algebraic framework for linear identification." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 151-168. <http://eudml.org/doc/244976>.

@article{Fliess2003,
abstract = {A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.},
affiliation = {Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique},
author = {Fliess, Michel, Sira-Ramírez, Hebertt},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {linear systems; identifiability; parametric identification; adaptive control; generalised proportional-integral controllers; module theory; differential algebra; operational calculus},
language = {eng},
pages = {151-168},
publisher = {EDP-Sciences},
title = {An algebraic framework for linear identification},
url = {http://eudml.org/doc/244976},
volume = {9},
year = {2003},
}

TY - JOUR
AU - Fliess, Michel
AU - Sira-Ramírez, Hebertt
TI - An algebraic framework for linear identification
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2003
PB - EDP-Sciences
VL - 9
SP - 151
EP - 168
AB - A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
LA - eng
KW - linear systems; identifiability; parametric identification; adaptive control; generalised proportional-integral controllers; module theory; differential algebra; operational calculus
UR - http://eudml.org/doc/244976
ER -

References

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  1. [1] K.J. Aström and T. Hägglund, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1998). 
  2. [2] K.J. Åstrom and B. Wittenmark, Adaptive Control, 2nd Ed. Addison-Wesley (1995). Zbl0697.93033
  3. [3] A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994). Zbl0870.12007MR1487891
  4. [4] R.R. Bitmead, M. Gevers and V. Wertz, Adaptive Optimal Control: The Thinking Man’s GPC. Prentice Hall (1990). Zbl0751.93052
  5. [5] P. Caines, Linear Stochastic Systems. Wiley (1988). Zbl0658.93003MR944080
  6. [6] S. Diop and M. Fliess, On nonlinear observability, in Proc. 1 s t Europ. Control Conf., edited by C. Commault, D. Normand–Cyrot, J.M. Dion, L. Dugard, M. Fliess, A. Titli, G. Cohen, A. Benveniste and I.D. Landau. Hermès (1991) 152-157. 
  7. [7] S. Diop and M. Fliess, Nonlinear observability, identifiability and persistent trajectories, in Proc. 36 t h IEEE Conf. Decision Control. Brighton (1991) 714-719. 
  8. [8] G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937). Zbl0018.12903JFM63.0368.01
  9. [9] M. Fliess, Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153. Zbl0764.93058MR1178584
  10. [10] M. Fliess and R. Marquez, Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Int. J. Control 73 (2000) 606-623. Zbl1006.93508MR1768024
  11. [11] M. Fliess and R. Marquez, Une approche intrinsèque de la commande prédictive linéaire discrète. APII J. Europ. Syst. Automat. 35 (2001) 127-147. 
  12. [12] M. Fliess, R. Marquez, E. Delaleau and H. Sira–Ramírez, Correcteurs proportionnels-intégraux généralisés. ESAIM: COCV 7 (2002) 23-41. Zbl1037.93040
  13. [13] M. Fliess and H. Sira–Ramírez, On the noncalibrated visual based control of planar manipulators: An on-line algebraic identification approach, in Proc. IEEE Conf. SMC. Hammamet, Tunisia (2002). 
  14. [14] T. Glad and L. Ljung, Control Theory: Multivariable and Nonlinear Methods. Taylor and Francis (2000). 
  15. [15] G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control. Prentice Hall (1984). Zbl0653.93001
  16. [16] L. Hsu and P. Aquino, Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera, in Proc. 38 t h IEEE Conf. Decision Control. Phoenix (1999) 1248-1253. 
  17. [17] R. Isermann, Identifikation dynamischer Systeme. Springer (1987). Zbl0756.93014
  18. [18] C.R. Johnson, Lectures on Adaptive Parameter Estimation. Prentice Hall (1988). Zbl0695.93001MR1010231
  19. [19] E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973). Zbl0264.12102MR568864
  20. [20] I.D. Landau, System Identification and Control Design. Prentice-Hall (1990). Zbl0751.93011
  21. [21] I.D. Landau and A. Besançon–Voda, Identification des systèmes. Hermès (2001). Zbl0897.93003
  22. [22] I.D. Landau, R. Lozano and M. M’Saad, Adaptive Control. Springer (1997). Zbl0885.93003
  23. [23] L. Ljung, System Identification: Theory for the User. Prentice-Hall (1987). Zbl0615.93004
  24. [24] L. Ljung and T. Glad, On global identifiability for arbitrary model parametrizations. Automatica 30 (1994) 265-276. Zbl0795.93026MR1261705
  25. [25] I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhäuser (1996). Zbl0923.93028MR1412576
  26. [26] J.C. McConnell and J.C. Robson, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000). Zbl0980.16019MR1811901
  27. [27] J. Mikusiński, Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983). Zbl0532.44003MR737380
  28. [28] J. Mikusiński and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987). Zbl0643.44005MR902363
  29. [29] K. Narenda and A. Annaswamy, Stable Adaptive Control. Prentice Hall (1989). 
  30. [30] F. Ollivier, Le problème de l’identifiabilité globale : étude théorique, méthodes effectives et bornes de complexité, Thèse. École Polytechnique, Palaiseau (1990). 
  31. [31] J. Richalet, Pratique de l’identification, 2 e Éd. Hermès (1998). Zbl0864.93002
  32. [32] A. Robinson, Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456. Zbl0106.25803MR122815
  33. [33] S. Sastry and M. Bodson, Adaptive Control. Prentice Hall (1989). Zbl0721.93046
  34. [34] A. Sedoglavic, Méthodes seminumériques en algèbre différentielle ; applications à l’étude des propriétés structurelles de systèmes différentiels algébriques en automatique, Thèse. École polytechnique, Palaiseau (2001). 
  35. [35] H. Sira–Ramírez, E. Fossas and M. Fliess, Output trajectory tracking in an uncertain double bridge “buck” dc to dc power converter: An algebraic on-line parameter identification approach, in Proc. 41 s t IEEE Conf. Decision Control (2002). 
  36. [36] H. Sira–Ramírez and M. Fliess, On the discrete-time uncertain visual based control of planar manipulators: An on-line algebraic identification approach, in Proc. 41 s t IEEE Conf. Decision Control (2002). 
  37. [37] P. Söderström and P. Stoica, System Identification. Prentice-Hall (1989). Zbl0695.93108
  38. [38] J.-C. Trigeassou, Contribution à l’extension de la méthode des moments en automatique. Application à l’identification des systèmes linéaires, Thèse d’État. Université de Poitiers (1987). 
  39. [39] É. Walter, Identifiability of State Space Models. Springer (1982). Zbl0508.93001MR672773
  40. [40] É. Walter, L. Pronzato, Identification des modèles paramétriques. Masson (1994). MR1306056
  41. [41] K. Yosida, Operational Calculus. Springer (1984). Zbl0542.44001MR752699

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