Observer design using a partial nonlinear observer canonical form

Röbenack, Klaus ; Lynch, Alan

International Journal of Applied Mathematics and Computer Science, Tome 16 (2006), p. 333-343 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the advantages of the approach relative to the existing nonlinear observer design methods. The advantages of the proposed method include a relatively simple design procedure which can be broadly applied.

Détail

Publié le : 2006-01-01

Zbl 1136.93313

EUDML-ID : urn:eudml:doc:207797

Bibliographie

[000] Amicucci G. L. and Monaco S. (1998): On nonlinear detectability. - J. Franklin Inst. 335B, Vol. 6, pp. 1105-1123. | Zbl 1030.93006

[001] Bestle D. and Zeitz M. (1983): Canonical form observer design for non-linear time-variable systems. - Int. J. Contr., Vol. 38, No. 2, pp. 419-431. | Zbl 0521.93012

[002] Birk J. and Zeitz M. (1988): Extended Luenberger observer for non-linear multivariable systems. - Int. J. Contr., Vol. 47,No. 6, pp. 1823-1836. | Zbl 0648.93022

[003] Brunovsky P. (1970): A classification of linear controllable systems.- Kybernetica, Vol. 6, No. 3, pp. 173-188. | Zbl 0199.48202

[004] Gauthier J. P., Hammouri H. and Othman S. (1992): A simple observer for nonlinear systems - Application to bioreactors.- IEEE Trans. Automat. Contr., Vol. 37, No. 6, pp. 875-880. | Zbl 0775.93020

[005] Hermann R. and Krener A. J. (1977): Nonlinear controllability and observability. - IEEE Trans. Automat. Contr., Vol. AC-22, No.5, pp. 728-740. | Zbl 0396.93015

[006] Isidori A. (1995): Nonlinear Control Systems: An Introduction, 3-rd Edn. - London: Springer.

[007] Jo N. H. and Seo J. H. (2002): Observer design for non-linear systems that are not uniformly observable. - Int. J. Contr.,Vol. 75, No. 5, pp. 369-380. | Zbl 1059.93021

[008] Kazantzis N. and Kravaris C. (1998): Nonlinear observer design using Lyapunov's auxiliary theorem. - Syst. Contr. Lett.,Vol. 34, pp. 241-247. | Zbl 0909.93002

[009] Keller H. (1986): Entwurf nichtlinearer Beobachter mittels Normalformen. - Dusseldorf: VDI-Verlag.

[010] Krener A. and Xiao M. (2002): Nonlinear observer design in the siegel domain. - SIAM J. Contr. Optim., Vol. 41, No. 3, pp. 932-953. | Zbl 1052.93013

[011] Krener A., Hubbard M., Karaham S., Phelps A. and Maag B. (1991): Poincare's linearization method applied to the design of nonlinear compensators. - Proc. Algebraic Computing in Control, Vol. 165 of Lecture Notes in Control and Information Science, Berlin: Springer, pp. 76-114. | Zbl 0793.93047

[012] Krener A. J. and Isidori A. (1983): Linearization by output injection and nonlinear observers. - Syst. Contr. Lett., Vol. 3, pp. 47-52. | Zbl 0524.93030

[013] Krener A. J. and Respondek W. (1985): Nonlinear observers with linearizable error dynamics. - SIAM J. Contr. Optim.,Vol. 23, No. 2, pp. 197-216. | Zbl 0569.93035

[014] Lynch A. and Bortoff S. (2001): Nonlinear observers with approximately linear error dynamics: The multivariable case.- IEEE Trans. Automat. Contr., Vol. 46, No. 7, pp. 927-932. | Zbl 1037.93014

[015] Marino R. and Tomei P. (1995): Nonlinear Control Design: Geometric, Adaptive and Robust. - London: Prentice Hall. | Zbl 0833.93003

[016] Moore E. H. (1920): On the reciprocal of the general algebraic matrix.- Bull. Amer. Math. Soc., Vol. 26, pp. 394-395.

[017] Mukhopadhyay B. K. and Malik O. P. (1972): Optimal control of synchronous-machine excitation by quasilinearisation techniques.- Proc. IEE, Vol. 119, No. 1, pp. 91-98.

[018] Nijmeijer H. and van der Schaft A. J. (1990): Nonlinear Dynamical Control Systems. - New York: Springer. | Zbl 0701.93001

[019] Phelps A. R. (1991): On constructing nonlinear observers.- SIAM J. Contr. Optim., Vol. 29, No. 3, pp. 516-534. | Zbl 0738.93032

[020] Respondek W. (1986): Global aspects of linearization, equivalence to polynomial forms and decomposition of nonlinear control systems. - Proc. Algebraic and Geometric Methods in Nonlinear Control, Dordrecht: Reidel, pp. 257-284. | Zbl 0605.93033

[021] Respondek W., Pogromsky A. and Nijmeijer H. (2004): Time scaling for observer design with linearizable error dynamics. - Automatica, Vol. 40, No. 2, pp. 277-285. | Zbl 1055.93010

[022] Rbenack K. and Lynch A. F. (2004): High-gain nonlinear observer design using the observer canonical form. - J. Franklin Institute, submitted.

[023] Rudolph J. and Zeitz M. (1994): A block triangular nonlinear observer normal form. - Syst. Contr. Lett., Vol. 23, pp. 1-8. | Zbl 0818.93006

[024] Schweitzer G., Bleuler H. and Traxler A. (1994): Active Magnetic Bearings. - Zurich: VDF .

[025] Shim H., Son Y. I. and Seo J. H. (2001): Semi-global observer for multi-output nonlinear systems. - Syst. Contr. Lett., Vol. 42,No. 3, pp. 233-244. | Zbl 0985.93006

[026] Sontag E. D. and Wang Y. (1997): Output-to-state stability and detectability of nonlinear system. - Syst. Contr. Lett., Vol. 29, No. 5, pp. 279-290. | Zbl 0901.93062

[027] Wang Y. and Lynch A. (2005): Block triangular observer forms for nonlinear observer design. - Automatica, (submitted).

[028] Wang Y. and Lynch A. (2006): A block triangular form for nonlinear observer design. - IEEE Trans. Automat. Contr., (to appear). | Zbl 1152.93319

[029] Xia X.-H. and Gao W.-B. (1988): Non-linear observer design by observer canonical form. - Int. J. Contr., Vol. 47, No. 4, pp. 1081-1100. | Zbl 0643.93011

[030] Xia X. H. and Gao W. B. (1989): Nonlinear observer design by observer error linearization. - SIAM J. Contr. Optim., Vol. 27, No. 1, pp. 199-216. | Zbl 0667.93014