Abstract
A few years ago the present authors launched a new approach to parametric identification of linear continuous-time systems [11]. Its main features may be summarised as follows:
-
closed-loop identification is permitted thanks to the real-time identification scheme;
-
the robustness with respect to noisy data is obtained without knowing the statistical properties of the corrupting noises.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K.J. Åström and B. Wittenmark. Adaptive Control. Addison Wesley, New York, 2nd edition, 1995.
H. Bourlès. Systèmes Linéaires: de la Modélisation à la Commande. Hermès, Paris, 2006.
G. Doetsch. Introduction to the Theory and Application of the Laplace Transform. Translated from the German. Springer, Berlin, 1974.
M. Fliess. Some basic structural properties of generalized linear systems. Systems Control Letters, 15:391–396, 1990.
M. Fliess. Une interprétation algébrique de la transformation de Laplace et des matrices de transfert. Linear Algebra and its Applications, 203–204:429–442, 1994.
M. Fliess. Analyse non standard du bruit. Comptes rendus de l’Académie des sciences, Paris Série I, 342:797–802, 2006.
M. Fliess, S. Fuchshumer, K. Schlacher, and H. Sira-Ramírez. Discrete-time linear parametric identification: An algebraic approach. 2 es Journées Identifi-cation et Modélisation Expérimentale, JIME’2006, Poitiers, 2006 (available at http://hal.inria.fr/inria-00105673).
M. Fliess, C. Join, and H. Sira-Ramírez. Robust residual generation for linear fault diagnosis: an algebraic setting with examples. International Journal of Control, 77:1223–1242, 2004.
M. Fliess and R. Marquez. Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. International Journal of Control, 73:606–623, 2000.
M. Fliess, R. Marquez, E. Delaleau, and H. Sira-Ramírez. Correcteurs proportionnels-intégraux généralisés. ESAIM: Control, Optimisation and Calculus of Variations, 7:23–41, 2002.
M. Fliess and H. Sira-Ramírez. An algebraic framework for linear identification. ESAIM: Control, Optimisation and Calculus of Variations, 9:151–168, 2003.
M. Fliess and H. Sira-Ramírez. Reconstructeurs d’état. Comptes rendus de l’Académie des sciences, Paris Série I, 338:91–96, 2004.
H. Garnier, M. Mensler, and A. Richard. Continuous-time model identification from sampled data: implementation issues and performance evaluation. International Journal of Control, 76:1337–1357, 2003.
G. Goodwin and D. Mayne. A parameter estimation perspective to continuous time model reference adaptive control. Automatica, 23:57–70, 1987.
P. Van den Hof. Closed-loop issues in system identification. Annual Reviews in Control, 22:173–1186, 1998.
L. Jaulin, M. Kieffer, O. Didrit, and E. Walter. Applied Interval: with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, Berlin, 2001.
S. Lang. Algebra. Springer, Berlin, 3rd edition, 2002.
E.K. Larsson, M. Mossberg, and T. Soderstrom. An overview of important practical aspects of continuous-time ARMA system identification. Circuits, Systems & Signal Processing, 25:17–46, 2006.
K. Mahata and H. Garnier. Identification of continuous-time errors-in-variable models. Automatica, 42:1470–1490, 2006.
J. McConnel and J. Robson. Noncommutative Noetherian Rings. Amer. Math. Soc., Providence, RI, 2000.
J. Mikusinski. Operational Calculus. Vol. 1, PWN & Pergamon, Warsaw & Oxford, 2nd edition, 1983.
J. Mikusinski and T. Boehme. Operational Calculus. Vol. 2, PWN & Pergamon, Warsaw & Oxford, 2nd edition, 1987.
K. Narendra and A. Annaswamy. Stable Adaptive Systems. Prentice Hall, Englewood Cliffs, 1989.
M. Phan, L. Horta, and R. Longman. Linear system identification via an asymptotically stable observer. Journal of Optimization Theory and Applications, 79:59–86, 1993.
B. van der Pol and H. Bremmer. Operational Calculus Based on the Two-Sided Laplace Integral. Cambridge University Press, Cambridge, 2nd edition, 1955.
T.I. Salsbury. Continuous-time model identification for closed loop control performance assessment. Control Engineering Practice, 15:109–121, 2007.
S. Sastry and M. Bodson. Adaptive Systems: Stability, Convergence and Robustness. Prentice Hall, Englewood Cliffs, 1989.
H. Sira-Ramírez and S.K. Agrawal. Differentially Flat Systems. Marcel Dekker, New York, 2004.
H. Sira-Ramírez, E. Fossas, and M. Fliess. An algebraic, on-line, parameter identification approach to uncertain dc-to-ac power conversion. 41 st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, 2002.
H. Sira-Ramírez and R. Silva-Ortigoza. Control Design Techniques in Power Electronics Devices. Springer, London, 2006.
J.-C. Trigeassou. Identification et commande des processus mono-entrée monosortie par la méthode des moments-Expérimentation sur calculatrice programmable. Thèse 3e cycle, Université de Nantes, 1980.
K. Yosida. Operational Calculus. Springer, New York, 1984.
P.C. Young. Parameter estimation for continuous-time models — a survey. Automatica, 17:23–39, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag London Limited
About this chapter
Cite this chapter
Fliess, M., Sira-Ramírez, H. (2008). Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques. In: Garnier, H., Wang, L. (eds) Identification of Continuous-time Models from Sampled Data. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-84800-161-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-84800-161-9_13
Publisher Name: Springer, London
Print ISBN: 978-1-84800-160-2
Online ISBN: 978-1-84800-161-9
eBook Packages: EngineeringEngineering (R0)