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An algebraic framework for linear identification

Published online by Cambridge University Press:  15 September 2003

Michel Fliess  and
Hebertt Sira–Ramírez
Michel Fliess
Affiliation:
Centre de Mathématiques et leurs Applications, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan, France; fliess@cmla.ens-cachan.fr.. Laboratoire GAGE, École Polytechnique, 91128 Palaiseau, France; fliess@gage.polytechnique.fr.
Hebertt Sira–Ramírez
Affiliation:
Cinvestav-IPN, Avenida IPN No. 2508, Departamento de Ingeniería Eléctrica, Sección de Mecatrónica, Colonia San Pedro Zacatenco, AP 14740, 07300 México, D.F., México; hsira@mail.cinvestav.mx..
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Abstract

A closed loop parametrical identification procedure forcontinuous-time constant linear systems is introduced. Thisapproach which exhibits good robustness properties with respect toa large variety of additive perturbations is based on thefollowing mathematical tools:(1) module theory;(2) differential algebra;(3) operational calculus.Several concrete case-studies with computer simulationsdemonstrate the efficiency of our on-line identification scheme.

Keywords

Linear systemsidentifiabilityparametricidentificationadaptive controlgeneralisedproportional-integral controllersmodule theorydifferentialalgebraoperational calculus.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 151 - 168
Copyright
© EDP Sciences, SMAI, 2003

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References

K.J. Aström and T. Hägglund, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1998).
K.J. Åstrom and B. Wittenmark, Adaptive Control, 2nd Ed. Addison-Wesley (1995).
A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994).
R.R. Bitmead, M. Gevers and V. Wertz, Adaptive Optimal Control: The Thinking Man's GPC. Prentice Hall (1990).
P. Caines, Linear Stochastic Systems. Wiley (1988).
S. Diop and M. Fliess, On nonlinear observability, in Proc. 1 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. Hermès (1991) 152-157.
S. Diop and M. Fliess, Nonlinear observability, identifiability and persistent trajectories, in Proc. 36 th IEEE Conf. Decision Control. Brighton (1991) 714-719.
G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937).
Fliess, M., Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153. CrossRef
Fliess, M. and Marquez, R., Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Int. J. Control 73 (2000) 606-623. CrossRef
Fliess, M. and Marquez, R., Une approche intrinsèque de la commande prédictive linéaire discrète. APII J. Europ. Syst. Automat. 35 (2001) 127-147.
Fliess, M., Marquez, R., Delaleau, E. and Sira-Ramírez, H., Correcteurs proportionnels-intégraux généralisés. ESAIM: COCV 7 (2002) 23-41. CrossRef
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).
T. Glad and L. Ljung, Control Theory: Multivariable and Nonlinear Methods. Taylor and Francis (2000).
G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control. Prentice Hall (1984).
L. Hsu and P. Aquino, Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera, in Proc. 38 th IEEE Conf. Decision Control. Phoenix (1999) 1248-1253.
R. Isermann, Identifikation dynamischer Systeme. Springer (1987).
C.R. Johnson, Lectures on Adaptive Parameter Estimation. Prentice Hall (1988).
E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973).
I.D. Landau, System Identification and Control Design. Prentice-Hall (1990).
I.D. Landau and A. Besançon-Voda, Identification des systèmes. Hermès (2001).
I.D. Landau, R. Lozano and M. M'Saad, Adaptive Control. Springer (1997).
L. Ljung, System Identification: Theory for the User. Prentice-Hall (1987).
Ljung, L. and Glad, T., On global identifiability for arbitrary model parametrizations. Automatica 30 (1994) 265-276. CrossRef
I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhäuser (1996).
J.C. McConnell and J.C. Robson, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000).
J. Mikusinski, Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983).
J. Mikusinski and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987).
K. Narenda and A. Annaswamy, Stable Adaptive Control. Prentice Hall (1989).
F. Ollivier, Le problème de l'identifiabilité globale : étude théorique, méthodes effectives et bornes de complexité, Thèse. École Polytechnique, Palaiseau (1990).
J. Richalet, Pratique de l'identification, $2\rm ^e$ Éd. Hermès (1998).
Robinson, A., Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456. CrossRef
S. Sastry and M. Bodson, Adaptive Control. Prentice Hall (1989).
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).
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 st IEEE Conf. Decision Control (2002).
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 st IEEE Conf. Decision Control (2002).
P. Söderström and P. Stoica, System Identification. Prentice-Hall (1989).
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).
É. Walter, Identifiability of State Space Models. Springer (1982).
É. Walter, L. Pronzato, Identification des modèles paramétriques. Masson (1994).
K. Yosida, Operational Calculus. Springer (1984).