Geodesic
Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms
Kybernetika, Tome 51 (2015) no. 1, pp. 36-58
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Necessary and sufficient conditions are given for the existence of state and output transformations, that bring single-input single-output nonlinear state equations into the observer form. The conditions are formulated in terms of differential one-forms, associated with an input-output equation of the system. An algorithm for transformation of the state equations into the observer form is presented and illustrated by an example.
Necessary and sufficient conditions are given for the existence of state and output transformations, that bring single-input single-output nonlinear state equations into the observer form. The conditions are formulated in terms of differential one-forms, associated with an input-output equation of the system. An algorithm for transformation of the state equations into the observer form is presented and illustrated by an example.
DOI : 10.14736/kyb-2015-1-0036
Classification : 93B10, 93B17, 93C10
Keywords: nonlinear control system; state and output transformations; observer form; differential one-form 
@article{10_14736_kyb_2015_1_0036,
     author = {Kaparin, Vadim and Kotta, \"Ulle},
     title = {Transformation of nonlinear state equations into the observer form: {Necessary} and sufficient conditions in terms of one-forms},
     journal = {Kybernetika},
     pages = {36--58},
     year = {2015},
     volume = {51},
     number = {1},
     doi = {10.14736/kyb-2015-1-0036},
     mrnumber = {3333832},
     zbl = {06433831},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-1-0036/}
}
TY  - JOUR
AU  - Kaparin, Vadim
AU  - Kotta, Ülle
TI  - Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms
JO  - Kybernetika
PY  - 2015
SP  - 36
EP  - 58
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-1-0036/
DO  - 10.14736/kyb-2015-1-0036
LA  - en
ID  - 10_14736_kyb_2015_1_0036
ER  - 
%0 Journal Article
%A Kaparin, Vadim
%A Kotta, Ülle
%T Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms
%J Kybernetika
%D 2015
%P 36-58
%V 51
%N 1
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-1-0036/
%R 10.14736/kyb-2015-1-0036
%G en
%F 10_14736_kyb_2015_1_0036
Kaparin, Vadim; Kotta, Ülle. Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms. Kybernetika, Tome 51 (2015) no. 1, pp. 36-58. doi: 10.14736/kyb-2015-1-0036

[1] Besançon, G.: On output transformations for state linearization up to output injection. IEEE Trans. Automat. Control 44 (1999), 10, 1975-1981. | DOI | MR | Zbl

[2] Bestle, D., Zeitz, M.: Canonical form observer design for non-linear time-variable systems. Int. J. Control 38 (1983), 2, 419-431. | DOI

[3] Boutat, D., Benali, A., Hammouri, H., Busawon, K.: New algorithm for observer error linearization with a diffeomorphism on the outputs. Automatica 45 (2009), 10, 2187-2193. | DOI | MR | Zbl

[4] Chiasson, J.: Nonlinear differential-geometric techniques for control of a series DC motor. IEEE Trans. Control Systems Technol. 2 (1994), 1, 35-42. | DOI

[5] Conte, G., Moog, C. H., Perdon, A. M.: Algebraic Methods for Nonlinear Control Systems. Theory and Applications. Second edition. Springer-Verlag, London 2007. | DOI | MR

[6] Glumineau, A., Moog, C. H., Plestan, F.: New algebro-geometric conditions for the linearization by input-output injection. IEEE Trans. Automat. Control 41 (1996), 4, 598-603. | DOI | MR | Zbl

[7] Guay, M.: Observer linearization by output-dependent time-scale transformations. IEEE Trans. Automat. Control 47 (2002), 10, 1730-1735. | DOI | MR

[8] Halás, M., Kotta, Ü: A transfer function approach to the realisation problem of nonlinear systems. Int. J. Control 85 (2012), 3, 320-331. | DOI | MR | Zbl

[9] Technology, Institute of Cybernetics at Tallinn University of: NLControl website. (2014). DOI 

[10] Isidori, A.: Nonlinear Control Systems: An Introduction. Lect. Notes Control Inform. Sci. 72, Springer-Verlag, Berlin 1985. | DOI | MR | Zbl

[11] Johnson, W. P.: The curious history of Faà di Bruno's formula. Amer. Math. Monthly 109 (2002), 3, 217-234. | DOI | MR | Zbl

[12] Jouan, P.: Immersion of nonlinear systems into linear systems modulo output injection. SIAM J. Control Optim. 41 (2003), 6, 1756-1778. | DOI | MR | Zbl

[13] Kaparin, V., Kotta, Ü.: Necessary and sufficient conditions in terms of differential-forms for linearization of the state equations up to input-output injections. In: UKACC International Conference on CONTROL 2010 (K. J. Burnham and V. E. Ersanilli, eds.), IET, Coventry 2010, pp. 507-511. | DOI

[14] Kaparin, V., Kotta, Ü.: Theorem on the differentiation of a composite function with a vector argument. Proc. Est. Acad. Sci. 59 (2010), 3, 195-200. | DOI | MR | Zbl

[15] Krener, A. J., Isidori, A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 1, 47-52. | DOI | MR | Zbl

[16] Krener, A. J., Respondek, W.: Nonlinear observers with linearizable error dynamics. SIAM J. Control Optim. 23 (1985), 2, 197-216. | DOI | MR | Zbl

[17] Mullari, T., Kotta, Ü.: Transformation the nonlinear system into the observer form: Simplification and extension. Eur. J. Control 15 (2009), 2, 177-183. | DOI | MR | Zbl

[18] Noh, D., Jo, N. H., Seo, J. H.: Nonlinear observer design by dynamic observer error linearization. IEEE Trans. Automat. Control 49 (2004), 10, 1746-1750. | DOI | MR

[19] Respondek, W., Pogromsky, A., Nijmeijer, H.: Time scaling for observer design with linearizable error dynamics. Automatica 40 (2004), 2, 277-285. | DOI | MR | Zbl

[20] Tõnso, M., Rennik, H., Kotta, Ü.: WebMathematica-based tools for discrete-time nonlinear control systems. Proc. Est. Acad. Sci. 58 (2009), 4, 224-240. | DOI | MR | Zbl

Cité par Sources :