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.
Mots-clés : linear systems, identifiability, parametric identification, adaptive control, generalised proportional-integral controllers, module theory, differential algebra, operational calculus
@article{COCV_2003__9__151_0,
author = {Fliess, Michel and Sira-Ram{\'\i}rez, Hebertt},
title = {An algebraic framework for linear identification},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {151--168},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003008},
zbl = {1063.93014},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2003008/}
}
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 SP - 151 EP - 168 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003008/ DO - 10.1051/cocv:2003008 LA - en ID - COCV_2003__9__151_0 ER -
%0 Journal Article %A Fliess, Michel %A Sira-Ramírez, Hebertt %T An algebraic framework for linear identification %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 151-168 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2003008/ %R 10.1051/cocv:2003008 %G en %F COCV_2003__9__151_0
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] and, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1998).
[2] and, Adaptive Control, 2nd Ed. Addison-Wesley (1995). | Zbl
[3] , Differential Algebra and Diophantine Geometry. Hermann (1994). | MR | Zbl
[4] , and, Adaptive Optimal Control: The Thinking Man's GPC. Prentice Hall (1990). | Zbl
[5] , Linear Stochastic Systems. Wiley (1988). | MR | Zbl
[6] and, On nonlinear observability1991) 152-157.
[7] and, Nonlinear observability, identifiability and persistent trajectories1991) 714-719.
[8] , Theorie und Anwendung der Laplace-Transformation. Springer (1937). | JFM | Zbl
[9] , Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153. | MR | Zbl
[10] and, Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Int. J. Control 73 (2000) 606-623. | MR | Zbl
[11] and, Une approche intrinsèque de la commande prédictive linéaire discrète. APII J. Europ. Syst. Automat. 35 (2001) 127-147.
[12] ,, and, Correcteurs proportionnels-intégraux généralisés. ESAIM: COCV 7 (2002) 23-41. | EuDML | Numdam | Zbl
[13] and, On the noncalibrated visual based control of planar manipulators: An on-line algebraic identification approach, in Proc. IEEE Conf. SMC. Hammamet, Tunisia (2002).
[14] and, Control Theory: Multivariable and Nonlinear Methods. Taylor and Francis (2000).
[15] and, Adaptive Filtering Prediction and Control. Prentice Hall (1984). | Zbl
[16] and, Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera1999) 1248-1253.
[17] , Identifikation dynamischer Systeme. Springer (1987). | Zbl
[18] , Lectures on Adaptive Parameter Estimation. Prentice Hall (1988). | MR | Zbl
[19] , Differential Algebra and Algebraic Groups. Academic Press (1973). | MR | Zbl
[20] , System Identification and Control Design. Prentice-Hall (1990).
[21] and, Identification des systèmes. Hermès (2001). | Zbl
[22] , and, Adaptive Control. Springer (1997). | Zbl
[23] , System Identification: Theory for the User. Prentice-Hall (1987). | Zbl
[24] and, On global identifiability for arbitrary model parametrizations. Automatica 30 (1994) 265-276. | MR | Zbl
[25] and, Adaptive Systems. An Introduction. Birkhäuser (1996). | MR | Zbl
[26] and, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000). | MR | Zbl
[27] , Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983). | MR | Zbl
[28] and, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987). | MR | Zbl
[29] and, Stable Adaptive Control. Prentice Hall (1989).
[30] , Le problème de l'identifiabilité globale : étude théorique, méthodes effectives et bornes de complexité, Thèse. École Polytechnique, Palaiseau (1990).
[31] , Pratique de l’identification, Éd. Hermès (1998). | Zbl
[32] , Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456. | MR | Zbl
[33] and, Adaptive Control. Prentice Hall (1989). | Zbl
[34] , Méthodes seminumériques en algèbre différentielle ; applications à l'étude des propriétés structurelles de systèmes différentiels algébriques en automatique, Thèse. École polytechnique, Palaiseau (2001).
[35] , and, Output trajectory tracking in an uncertain double bridge “buck” dc to dc power converter: An algebraic on-line parameter identification approach2002).
[36] and, On the discrete-time uncertain visual based control of planar manipulators: An on-line algebraic identification approach2002).
[37] and, System Identification. Prentice-Hall (1989). | Zbl
[38] , 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] , Identifiability of State Space Models. Springer (1982). | MR
[40] ,, Identification des modèles paramétriques. Masson (1994). | MR
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