An algebraic framework for linear identification
Michel Fliess; Hebertt Sira-Ramírez[1]
- [1] Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique
ESAIM: Control, Optimisation and Calculus of Variations (2003)
- Volume: 9, page 151-168
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topFliess, Michel, and Sira-Ramírez, Hebertt. "An algebraic framework for linear identification." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 151-168. <http://eudml.org/doc/244976>.
@article{Fliess2003,
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.},
affiliation = {Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique},
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},
language = {eng},
pages = {151-168},
publisher = {EDP-Sciences},
title = {An algebraic framework for linear identification},
url = {http://eudml.org/doc/244976},
volume = {9},
year = {2003},
}
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
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
UR - http://eudml.org/doc/244976
ER -
References
top- [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). Zbl0697.93033
- [3] A. Buium, Differential Algebra and Diophantine Geometry. Hermann (1994). Zbl0870.12007MR1487891
- [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). Zbl0658.93003MR944080
- [6] S. Diop and M. Fliess, On nonlinear observability, in Proc. 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. IEEE Conf. Decision Control. Brighton (1991) 714-719.
- [8] G. Doetsch, Theorie und Anwendung der Laplace-Transformation. Springer (1937). Zbl0018.12903JFM63.0368.01
- [9] M. Fliess, Reversible linear and nonlinear discrete-time dynamics, IEEE Trans. Automat. Control 37 (1992) 1144-1153. Zbl0764.93058MR1178584
- [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. Zbl1006.93508MR1768024
- [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. Zbl1037.93040
- [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. 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). Zbl0695.93001MR1010231
- [19] E.R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press (1973). Zbl0264.12102MR568864
- [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). Zbl0897.93003
- [22] I.D. Landau, R. Lozano and M. M’Saad, Adaptive Control. Springer (1997). Zbl0885.93003
- [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. Automatica 30 (1994) 265-276. Zbl0795.93026MR1261705
- [25] I. Mareels and J.W. Polderman, Adaptive Systems. An Introduction. Birkhäuser (1996). Zbl0923.93028MR1412576
- [26] J.C. McConnell and J.C. Robson, Noncommutative Noetherian Rings. Amer. Math. Soc. (2000). Zbl0980.16019MR1811901
- [27] J. Mikusiński, Operational Calculus, 2nd Ed., Vol. 1. PWN & Pergamon (1983). Zbl0532.44003MR737380
- [28] J. Mikusiński and T.K. Boehme, Operational Calculus, 2nd Ed., Vol. 2. PWN & Pergamon (1987). Zbl0643.44005MR902363
- [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, Éd. Hermès (1998). Zbl0864.93002
- [32] A. Robinson, Local differential algebra. Trans. Amer. Math. Soc. 97 (1960) 427-456. Zbl0106.25803MR122815
- [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. 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. 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). Zbl0508.93001MR672773
- [40] É. Walter, L. Pronzato, Identification des modèles paramétriques. Masson (1994). MR1306056
- [41] K. Yosida, Operational Calculus. Springer (1984). Zbl0542.44001MR752699
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.