An algebraic framework for linear identification

Michel Fliess; Hebertt Sira–Ramírez

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • 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 (2010): 151-168. <http://eudml.org/doc/90687>.

@article{Fliess2010,
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. },
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.; linear systems; parametric identification; generalised proportional-integral controllers; differential algebra; operational calculus},
language = {eng},
month = {3},
pages = {151-168},
publisher = {EDP Sciences},
title = {An algebraic framework for linear identification},
url = {http://eudml.org/doc/90687},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Fliess, Michel
AU - Sira–Ramírez, Hebertt
TI - An algebraic framework for linear identification
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
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.; linear systems; parametric identification; generalised proportional-integral controllers; differential algebra; operational calculus
UR - http://eudml.org/doc/90687
ER -

References

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  1. K.J. Aström and T. Hägglund, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1998).  
  2. K.J. Åstrom and B. Wittenmark, Adaptive Control, 2nd Ed. Addison-Wesley (1995).  
  3. A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994).  Zbl0870.12007
  4. R.R. Bitmead, M. Gevers and V. Wertz, Adaptive Optimal Control: The Thinking Man's GPC. Prentice Hall (1990).  Zbl0751.93052
  5. P. Caines, Linear Stochastic Systems. Wiley (1988).  Zbl0658.93003
  6. S. Diop and M. Fliess, On nonlinear observability, in Proc. 1st 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. S. Diop and M. Fliess, Nonlinear observability, identifiability and persistent trajectories, in Proc. 36thIEEE Conf. Decision Control. Brighton (1991) 714-719.  
  8. G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937).  Zbl63.0368.01
  9. M. Fliess, Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control37 (1992) 1144-1153.  Zbl0764.93058
  10. M. Fliess and R. Marquez, Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Int. J. Control73 (2000) 606-623.  Zbl1006.93508
  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. M. Fliess, R. Marquez, E. Delaleau and H. Sira-Ramírez, Correcteurs proportionnels-intégraux généralisés. ESAIM: COCV7 (2002) 23-41.  
  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. T. Glad and L. Ljung, Control Theory: Multivariable and Nonlinear Methods. Taylor and Francis (2000).  
  15. G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control. Prentice Hall (1984).  Zbl0653.93001
  16. L. Hsu and P. Aquino, Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera, in Proc. 38th IEEE Conf. Decision Control. Phoenix (1999) 1248-1253.  
  17. R. Isermann, Identifikation dynamischer Systeme. Springer (1987).  Zbl0756.93014
  18. C.R. Johnson, Lectures on Adaptive Parameter Estimation. Prentice Hall (1988).  Zbl0695.93001
  19. E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973).  Zbl0264.12102
  20. I.D. Landau, System Identification and Control Design. Prentice-Hall (1990).  Zbl0751.93011
  21. I.D. Landau and A. Besançon-Voda, Identification des systèmes. Hermès (2001).  
  22. I.D. Landau, R. Lozano and M. M'Saad, Adaptive Control. Springer (1997).  
  23. L. Ljung, System Identification: Theory for the User. Prentice-Hall (1987).  Zbl0615.93004
  24. L. Ljung and T. Glad, On global identifiability for arbitrary model parametrizations. Automatica30 (1994) 265-276.  Zbl0795.93026
  25. I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhäuser (1996).  Zbl0923.93028
  26. J.C. McConnell and J.C. Robson, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000).  
  27. J. Mikusinski, Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983).  Zbl0532.44003
  28. J. Mikusinski and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987).  Zbl0643.44005
  29. K. Narenda and A. Annaswamy, Stable Adaptive Control. Prentice Hall (1989).  
  30. F. Ollivier, Le problème de l'identifiabilité globale : étude théorique, méthodes effectives et bornes de complexité, Thèse. École Polytechnique, Palaiseau (1990).  
  31. J. Richalet, Pratique de l'identification, 2 e Éd. Hermès (1998).  
  32. A. Robinson, Local differential algebra. Trans. Amer. Math. Soc.97 (1960) 427-456.  Zbl0106.25803
  33. S. Sastry and M. Bodson, Adaptive Control. Prentice Hall (1989).  Zbl0721.93046
  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. 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. 41st IEEE Conf. Decision Control (2002).  
  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. 41st IEEE Conf. Decision Control (2002).  
  37. P. Söderström and P. Stoica, System Identification. Prentice-Hall (1989).  Zbl0695.93108
  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. É. Walter, Identifiability of State Space Models. Springer (1982).  Zbl0508.93001
  40. É. Walter, L. Pronzato, Identification des modèles paramétriques. Masson (1994).  
  41. K. Yosida, Operational Calculus. Springer (1984).  Zbl0538.44002

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