An algebraic framework for linear identification

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 9, Issue , 2003, Pages 151-168

  Fliess, Michel ^a,b   Sira Ramírez, Hebertt ^c  

^a Inserm   (United Kingdom)

^b ECOLE POLYTECHNIQUE   (France)

^c DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Adaptive control; Differential algebra; Generalised proportionalintegral controllers; Identifiability; Linear systems; Module theory; Operational calculus; Parametric identification

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS);

DIFFERENTIAL ALGEBRA; GENERALISED PROPORTIONAL INTEGRAL CONTROLLERS; MODULE THEORY; OPERATIONAL CALCULUS;

LINEAR SYSTEMS;

EID: 0142178909     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2003008     Document Type: Article

References (41)

1. K.J. Aström and T. Hagglund, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1998).
2. K.J. Astrom and B. Wittenmark, Adaptive Control, 2nd Ed. Addison-Wesley (1995).
3. A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994).
4. R.R. Bitmead, M. Gevers and V. Wertz, Adaptive Optimal Control: The Thinking Man’s GPC. Prentice Hall (1990).
5. P. Caines, Linear Stochastic Systems. Wiley (1988).
6. st 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. Hermes (1991) 152-157.
7. th IEEE Conf. Decision Control. Brighton (1991) 714-719.
8. G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937).
9. M. Fliess, Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153.
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.
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-Ramirez, Correcteurs proportionnels-integraux generalises. ESAIM: COCV 7 (2002) 23-41.
13. M. Fliess and H. Sira-Ramirez, 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).
16. th IEEE Conf. Decision Control. Phoenix (1999) 1248-1253.
17. R. Isermann, Identifikation dynamischer Systeme. Springer (1987).
18. C.R. Johnson, Lectures on Adaptive Parameter Estimation. Prentice Hall (1988).
19. E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973).
20. I.D. Landau, System Identification and Control Design. Prentice-Hall (1990).
21. I.D. Landau and A. Besancon-Voda, Identification des systemes. Hermes (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).
24. L. Ljung and T. Glad, On global identifiability for arbitrary model parametrizations. Automatica 30 (1994) 265-276.
25. I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhauser (1996).
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).
28. J. Mikusinski and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987).
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, These. Ecole Polytechnique, Palaiseau (1990).
31. e Ed. Hermes (1998).
32. A. Robinson, Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456.
33. S. Sastry and M. Bodson, Adaptive Control. Prentice Hall (1989).
34. A. Sedoglavic, Méthodes seminumériques en algèbre différentielle; applications à l’étude des propriétés structurelles de systèmes différentiels algébriques en automatique, These. Ecole polytechnique, Palaiseau (2001).
35. st IEEE Conf. Decision Control (2002).
36. st IEEE Conf. Decision Control (2002).
37. P. Soderstrom and P. Stoica, System Identification. Prentice-Hall (1989).
38. J.-C. Trigeassou, Contribution à l’extension de la méthode des moments en automatique. Application a l’identification des systèmes linéaires, These d’Etat. Universite de Poitiers (1987).
39. E. Walter, Identifiability of State Space Models. Springer (1982).
40. E. Walter, L. Pronzato, Identification des modèles parametriques. Masson (1994).
41. K. Yosida, Operational Calculus. Springer (1984).