An algebraic framework for linear identification
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 151-168.

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.

DOI : 10.1051/cocv:2003008
Classification : 93B30, 93B35, 93C05, 93C73, 93C95, 12H05, 13C05, 44A40
Mots clés : linear systems, identifiability, parametric identification, adaptive control, generalised proportional-integral controllers, module theory, differential algebra, operational calculus
Fliess, Michel  ; Sira-Ramírez, Hebertt 1

1 Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique
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Fliess, Michel; Sira-Ramírez, Hebertt. An algebraic framework for linear identification. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 151-168. doi : 10.1051/cocv:2003008. http://www.numdam.org/articles/10.1051/cocv:2003008/

[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). | Zbl

[3] A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994). | MR | Zbl

[4] R.R. Bitmead, M. Gevers and V. Wertz, Adaptive Optimal Control: The Thinking Man's GPC. Prentice Hall (1990). | Zbl

[5] P. Caines, Linear Stochastic Systems. Wiley (1988). | MR | Zbl

[6] S. Diop and M. Fliess, On nonlinear observability1991) 152-157.

[7] S. Diop and M. Fliess, Nonlinear observability, identifiability and persistent trajectories1991) 714-719.

[8] G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937). | JFM | Zbl

[9] M. Fliess, Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153. | MR | Zbl

[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. | MR | Zbl

[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: COCV 7 (2002) 23-41. | EuDML | Numdam | Zbl

[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). | Zbl

[16] L. Hsu and P. Aquino, Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera1999) 1248-1253.

[17] R. Isermann, Identifikation dynamischer Systeme. Springer (1987). | Zbl

[18] C.R. Johnson, Lectures on Adaptive Parameter Estimation. Prentice Hall (1988). | MR | Zbl

[19] E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973). | MR | Zbl

[20] I.D. Landau, System Identification and Control Design. Prentice-Hall (1990).

[21] I.D. Landau and A. Besançon-Voda, Identification des systèmes. Hermès (2001). | Zbl

[22] I.D. Landau, R. Lozano and M. M'Saad, Adaptive Control. Springer (1997). | Zbl

[23] L. Ljung, System Identification: Theory for the User. Prentice-Hall (1987). | Zbl

[24] L. Ljung and T. Glad, On global identifiability for arbitrary model parametrizations. Automatica 30 (1994) 265-276. | MR | Zbl

[25] I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhäuser (1996). | MR | Zbl

[26] J.C. Mcconnell and J.C. Robson, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000). | MR | Zbl

[27] J. Mikusiński, Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983). | MR | Zbl

[28] J. Mikusiński and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987). | MR | Zbl

[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). | Zbl

[32] A. Robinson, Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456. | MR | Zbl

[33] S. Sastry and M. Bodson, Adaptive Control. Prentice Hall (1989). | Zbl

[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 approach2002).

[36] H. Sira-Ramírez and M. Fliess, On the discrete-time uncertain visual based control of planar manipulators: An on-line algebraic identification approach2002).

[37] P. Söderström and P. Stoica, System Identification. Prentice-Hall (1989). | Zbl

[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). | MR

[40] É. Walter, L. Pronzato, Identification des modèles paramétriques. Masson (1994). | MR

[41] K. Yosida, Operational Calculus. Springer (1984). | MR | Zbl

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