UDK 519.711.3 DoI: 10.31772/2587-6066-2018-19-1-37-43
ABOUT NON-PARAMETRIC IDENTIFICATION OF T-PROCESSES
A. V. Medvedev1, D. I. Yareshchenko2*
1Reshetnev Siberian State University of Science and Technology 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation 2Siberian Federal University 26/1, Academician Kirensky St., Krasnoyarsk, 660074, Russian Federation *E-mail: YareshenkoDI@yandex.ru
This paper is devoted to the construction of a new class of models under incomplete information. We are talking about multidimensional inertia-free objects for the case when the components of the output vector are stochastically dependent, and the character of this dependence is unknown a priori. The study of a multidimensional object inevitably leads to a system of implicit dependencies of the output variables of the object from the input variables, but in this case this dependence extends to some components of the output vector. The key issue in this situation is the definition of the nature of this dependence for which the presence of a priori information is necessary to some extent. Taking into account that the main purpose of the model of such objects is the prediction of output variables with known input, it is necessary to solve a system of nonlinear implicit equations whose form is unknown at the initial stage of the identification problem, but only that one or another output component depends on other variables which determine the state of the object. Thus, a rather nontrivial situation arises for the solution of a system of implicit nonlinear equations under conditions when there are no usual equations. Consequently, the model of the object (and this is a main identification task) cannot be constructed in the same way as is accepted in the existing theory of identification as a result of a lack of a priori information. If it was possible to parametrize the system of nonlinear equations, then at a known input it would be necessary to solve this system, since in this case it is known, once the parameterization step is overcome. The main content of this article is the solution of the identification problem, in the presence of T-processes, and while the parametrization stage can not be overcome without additional a priori information about the process under investigation. In this connection, the scheme for solving a system of non-linear equations (which are unknown) can be represented in the form of some successive algorithmic chain. First, a vector of discrepancies is formed on the basis of the available training sample including observations of all components of the input and output variables. And after that, the evaluation of the output of the object with known values of the input variables is based on the Nadaraya-Watson estimates. Thus, for given values of the input variables of the T-process, we can carry out a procedure of estimating the forecast of the output variables. Numerous computational experiments on the study of the proposed T-models have shown their rather high efficiency. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology of forecasting the values of output variables on the known input.
discrete-continuous process, identification, T-models, T-processes.
References
1. Dub Dzh. L. Veroyatnostnye processy [Probabilistic process]. Moscow, Iz-vo inostrannoy literatury Publ., 1956, 605 p.
2. Medvedev A. V. Osnovy teorii adaptivnyh sistem: monografiya [Fundamentals of adaptive systems theory]. Krasnoyarsk, SibGAU Publ., 2015, 526 р.
3. Ehjkhoff P. Osnovy identifikacii sistem upravleniya [Basics of identification of control systems]. Moscow, Mir Publ., 1975, 7 p.
4. Cypkin Ya. Z. Osnovy informacionnoj teorii identifikacii [Fundamentals of information theory of identification]. Moscow, Nauka Publ., 1984, 320 p.
5. Nadaraya E. A. Neparametricheskoe ocenivanie plotnosti veroyatnostey i krivoy regressii [Nonparametric estimation of probability density and regression curve]. Tbilisi, Tbilisskiy universitet Publ., 1983, 194 p.
6. Vasil’ev V. A., Dobrovidov A. V., Koshkin G. M. Neparametricheskoe ocenivanie funkcionalov ot raspredeleniy stacionarnyh posledovatel’nostey [Nonparametric estimation of functionals of stationary sequences distributions]. Moscow, Nauka Publ., 2004, 508 p.
7. Sovetov B. Ya., Yakovlev S. A. Modelirovanie system [Modeling of systems]. Moscow, Vysshaya shkola Publ., 2001, 343 р.
8. Cypkin Y. Z. Adaptaciya i obuchenie v avtomaticheskih sistemah [Adaptation and training in automatic systems]. Moscow, Nauka Publ., 1968, 400 p.
9. Medvedev A. V. [The theory of non-parametric systems]. Vestnik SibGAU. 2010, No. 4 (30), P. 4–9 (In Russ.).
10. Fel’dbaum A. A. Osnovy teorii optimal’nyh avtomaticheskih system [Fundamentals of the theory of optimal automatic systems]. Moscow, Fizmatgiz Publ., 1963.
11. Medvedev A. V. Neparametricheskie sistemy adaptacii [Nonparametric adaptation systems]. Novosibirsk, Nauka Publ., 1983.
12. Medvedev A. V., Yareshchenko D. I. [About modeling of process of acquisition of knowledge by Output value Output value Model Model Object Object students at University]. Vysshee obrazovanie segodnya. 2017, No. 1, P. 7–10 (In Russ.).
13. Linnik Y. V. Metod naimen’shih kvadratov i osnovy teorii obrabotki nablyudeniy [The method of least squares and the foundations of the theory of processing observations]. Moscow, Fizmatlit Publ., 1958, 336 p.
14. Amosov N. M. Modelirovanie slozhnyh system [Modeling of complex systems]. Kiev, Naukova dumka Publ., 1968, 81 p.
15. Antomonov Y. G., Harlamov V. I. Kibernetika i zhizn’ [Cybernetics and life]. Moscow, Sov. Rossiya Publ., 1968, 327 p.
Medvedev Alexander Vasilievich – Dr. Sc., professor of Department of System Analysis and Operations Research,
Reshetnev Siberian State University of Science and Technology. E-mail: saor_medvedev@sibsau.ru.
Yareshchenko Darya Igorevna – senior teacher, Department of Intelligent Control Systems, Institute of Space and
Information Technologies, Siberian Federal University. E-mail: YareshenkoDI@yandex.ru.
