Geodesic
On approximate Takagi–Sugeno linear representations of nonlinear functions
Matematičeskoe modelirovanie, Tome 29 (2017) no. 1, pp. 20-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper discusses some methods of approximating a nonlinear function by a linear Takagi–Sugeno model, namely, by a convex combination of linear functions on a compact set. The known algorithms of approximating are considered as well as some new versions are proposed. They reduce both computational complexity and approximation error, and are applicable to a wider class of functions. The desired approximation is represented as a linear combination of the prescribed “basic” functions, which are assumed here to be the most commonly used in such models. We prove linear dependence of the basic functions and provide a linearly independent subsystem used for the proposed embodiments of the method of least squares. Discussion of the considered methods is presented. Also we calculate approximations for some functions of one and two variables to compare the maximum approximation errors and to see how the errors vary as we increase the number of the basic functions.
Keywords: nonlinear function, linear Takagi–Sugeno model, approximation, least squares method. 
@article{MM_2017_29_1_a1,
     author = {J. E. Egrashkina and N. O. Sedova},
     title = {On approximate {Takagi{\textendash}Sugeno} linear representations of nonlinear functions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {20--32},
     year = {2017},
     volume = {29},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_1_a1/}
}
TY  - JOUR
AU  - J. E. Egrashkina
AU  - N. O. Sedova
TI  - On approximate Takagi–Sugeno linear representations of nonlinear functions
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 20
EP  - 32
VL  - 29
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_1_a1/
LA  - ru
ID  - MM_2017_29_1_a1
ER  - 
%0 Journal Article
%A J. E. Egrashkina
%A N. O. Sedova
%T On approximate Takagi–Sugeno linear representations of nonlinear functions
%J Matematičeskoe modelirovanie
%D 2017
%P 20-32
%V 29
%N 1
%U http://geodesic.mathdoc.fr/item/MM_2017_29_1_a1/
%G ru
%F MM_2017_29_1_a1
J. E. Egrashkina; N. O. Sedova. On approximate Takagi–Sugeno linear representations of nonlinear functions. Matematičeskoe modelirovanie, Tome 29 (2017) no. 1, pp. 20-32. http://geodesic.mathdoc.fr/item/MM_2017_29_1_a1/

[1] K. Tanaka, N. O. Wang, Fuzzy control systems design and analysis: a linear matrix inequality approach, Wiley, N.Y., 2001, 305 pp.

[2] Zh. E. Egrashkina, “Tochnoe predstavlenie nelineinykh sistem obyknovennykh differentsialnykh uravnenii v vide nechetkikh lineinykh modelei Takagi–Sugeno”, Nauchno-tekhnicheskii vestnik Povolzhia, 2014, no. 2, 16–24

[3] M. Hamdy, I. Hamdan, “Robust fuzzy output feedback controller for affine nonlinear systems via TS fuzzy bilinear model: CSTR benchmark”, ISA Transactions, 2015, July, 1–8

[4] B. M. Al-Hadithi, A. Jimenez, F. Matia, “A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems”, Applied Soft Computing, 12:1 (2012), 280–290 | DOI

[5] P. Baranyi, “TP Model Transformation as a Manipulation Tool for QLPV Analysis and Design”, Asian Journal of Control, 17:2, March (2015), 497–507 | DOI | MR | Zbl