Abstract
Algorithms for the identification of continuous time nonlinear plants operating in open-loop and in closed-loop are presented. An adjustable output error type predictor is used in open-loop operation. An adjustable output error type predictor parametrized in terms of the existing controller and the estimated plant model is used in closed-loop operation. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Some convergence results based on passivity concepts are presented. Subsequently the algorithms are analyzed in the presence of noise and when the plant model is not in the model set. Examples illustrate the use of the various algorithms.
Preview
Unable to display preview. Download preview PDF.
References
B.D.O. Anderson. A system theory criterion for positive real matrices. SIAM Journal of Control, 5:171–182, 1967.
B.D.O Anderson and P.J. Maylan. Synthesis of linear time-varying passive networks. IEEE Transactions on Circuits and Systems, 21:678–687, 1974.
S. Dasgupta and B.D.O Anderson. A parametrization for the closed-loop identification of nonlinear time-varying systems. Automatica, 32:1349–1360, 1996.
F. De Bruyne, B.D.O Anderson and I.D. Landau. Closed-loop output error identification of nonlinear plants using kernel representations Submitted for the Conference on Decision and Control, Sydney, 2000.
C.A. Desoer and M. Vidyasagar. Feedback Systems: Input and Output Properties. Electrical Science Series, Academic Press, New York, 1975.
M. Kristic, I. Kanellakopoulos, and P. Kokotovic. Nonlinear and Adaptive Control Design. Wiley, New York, 1995.
I.D. Landau. Adaptive Control — The Model Reference Approach. M. Dekker, New York, 1979.
I.D. Landau and A. Karimi. Recursive algorithms for identification in closed-loop: A unified approach and evaluation. Automatica, 33:1499–1523, 1997.
I.D. Landau, R. Lozano, and M. M'saad. Adaptive Control. Springer Verlag, United Kingdom, 1997.
N. Linard, B.D.O. Anderson, and F. De Bruyne. Identification of a nonlinear plant under nonlinear feedback using left coprime fraction based representations. Automatica, 35:655–667, 1999.
L. Ljung. System Identification: Theory for the User. Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
L. Ljung and T. Soderstrom. Theory and Practice of Recursive Identification. MIT Press, Cambridge, Mass, 1983.
M. Gevers. Towards a joint design of identification and control? Essays on control: perspectives in the theory and its applications, H.L. Trentelman and J.C. Willems Editors, Birkhäuser, pages 111–151, 1993.
K.S. Narendra and A.M. Annaswamy. Stable adaptive systems. Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
V.M. Popov. Hyperstability of Automatic Control Systems. Springer Verlag, Berlin, 1973.
E.D. Sontag. On the input-to-state stability property. European Journal of Control, 1:24–35, 1995.
E.T. Van Donkelaar and P.M.J. Van den Hof. Analysis of closed-loop identification with a tailor-made parametrization. Selected Topics in Identification, Modelling and control, 9:17–24, 1996.
F. De Bruyne, B.D.O. Anderson, N. Linard, and M. Gevers. Gradient expressions for a closed-loop identification scheme with a tailor-made parametrization. Automatica, 35, 1999.
I.D. Landau, B.D.O. Anderson, and F. De Bruyne. Closed loop output error identification algorithms for nonlinear plants. Proc. IEEE-CDC 1999, 606–611, Phoenix Arizona, USA.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2001 Springer-Verlag London Limited
About this paper
Cite this paper
Landau, I.D., Anderson, B.D.O., De Bruyne, F. (2001). Algorithms for identification of continuous time nonlinear systems: a passivity approach. Part I: Identification in open-loop operation Part II: Identification in llosed-loop operation. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110289
Download citation
DOI: https://doi.org/10.1007/BFb0110289
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-364-5
Online ISBN: 978-1-84628-569-1
eBook Packages: Springer Book Archive