UDK 62-506.1 Vestnik SibGAU. 2014, No. 3(55), P. 93–99
NONPARAMETRIC MODELS OF THE HAMMERSTEIN DYNAMICAL OBJECTS
N. V. Koplyarova, N. A. Sergeeva
Siberian Federal University 79, Svobodnyi prosp., Krasnoyarsk, 660041, Russian Federation Е-mail: koplyarovanv@mail. ru
The problem of nonlinear dynamical systems of the Hammerstein type identification is considered. Systems in the conditions of partial parameterization are considered. In this case structure and parameters of equation, which de-scribe the linear dynamical part of the object, are unknown. The common type of nonlinearity is assumed to be known with the set of parameters. It is required to construct the mathematical model of the investigation system, which is based on the input-output measures sample. The proposed method of dynamic objects modeling is based on the nonparametric estimation of linear and nonlinear parts of the system. At first it is offered to estimate the nonlinear element parameters, and to the input of system consistently applied different input actions. Then the linear dynamical part model can be con-structed as a Duhamel integral, where the impulse response function is estimated with nonparametric algorithm. Pre-sented algorithm doesn’t require a complete priory information about the object structure. In the work the results of computer modeling of the Hammerstein type systems with the quard and the saturation nonlinearity are shown. This nonparametric model can describe the investigation systems with different types of nonlinearity, in conditions of noise in the measure channels, and with different sample sizes and input actions. The numerical researches show that the algorithms should be used to identify the Hammerstein type nonlinear systems.
Hammerstein model, nonparametric estimation, nonlinear dynamics, a priori information.
References

1. Cypkin Ja. Z. Osnovy informacionnoi teorii identificacii [Fundamentals of the informational theory of identification]. Moscow, Nauka Publ., 1984, 320 p.

2. Medvedev A. V. [Nonparametric algorithms of nonlinear dynamical system identification]. Stohasticheskie sistemi upravleniya [Stochastic control system]. Novosibirsk, Nauka Publ., 1979, p. 15–22.

3. Chaika S. N. [To dynamical systems of Hammerstein class identification with partially parameterized model structure]. Dinamica system: upravlenie i optimizaciya [System dynamics: Control and optimization]. Gorki, Gorki university Publ, 1989, p 24–36.

4. Nadaraya E. A. Neparametricheskoe ocenivanie plotnosti veroyatnosti I krivoi regressii [Nonparametric estimation of probability density function and regression curve]. Tbilissi, Tbilissi Univ. Publ, 1983, 194 p.

5. Popkov U. S. Identifikaciya I optimizaciya nelineinih stohasticheskih sistem [Identification and optimization of nonlinear stochastic systems]. Moscow, Energya Publ., 1976, 440 p.

6. Koplyarova N. V., Sergeeva N. A. [About the nonparametric algorithms of nonlinear dynamical processes identification]. Vestnic SibGAU, 2012, no. 5 (51), p. 39–44. (In Russ.)


Koplyarova Nadezhda Vladimirovna – postgraduate student, Siberian Federal University. E-mail: koplyarovanv@mail.ru

Sergeeva Natalia Alexandrovna – Candidate of Engineering sciences, associate professor of the Department of Informatics, Institution of Space and Information technologies, Siberian Federal University. Е-mail: sergena@list.ru