UDK 519.711.3 Doi: 10.31772/2587-6066-2020-21-1-47-53
ABOUT NON-PARAMETRIC IDENTIFICATION OF PARTIAL-PARAMETRED DISCRETE-CONTINUOUS PROCESS
Yareshchenko D. I.
Siberian Federal University, 26/1, Akademika Kirenskogo St., Krasnoyarsk, 660074, Russian Federation. E-mail: YareshenkoDI@yandex.ru
The paper considers a new class of models under conditions of incomplete information. We are talking about multidimensional discrete-continuous processes for the case where the components of the vector of output variables are stochastically dependent. The nature of this dependence is a priori unknown, but for some channels the a priori information corresponds to both nonparametric and parametric type of the initial data in the process under study. Such a situation leads to a system of nonlinear equations, some of which will be unknown, while others are known accurate to the vector of parameters. The main purpose of the model is to determine the forecast of output variables with known input, and for implicit nonlinear equations it is only known that one or another component of the output depends on other variables that determine the state of the object. Thus, a rather nontrivial situation arises when solving a system of implicit nonlinear equations under conditions where in one channel of a multidimensional system equations themselves are not in the usual sense, while in others they are known up to parameters. Therefore, an object model cannot be constructed using the methods of the existing identification theory as a result of a lack of a priori information. If it was possible to parameterize the system of nonlinear equations, then with a known input this system should be solved, since it is known and the parameterization stage is over. However, in this case it is still necessary to evaluate parameters. The main content of this article is the solution of the identification problem in the presence of a partially-parameterized discrete-continuous process, despite the fact that the parameterization stage cannot be overcome without additional a priori information on the process under study. In this regard, the scheme for solving the system of nonlinear equations can be represented as a certain sequential algorithmic chain. First, on the basis of the available training sample, including all components of the input and output variables observation, a residual vector is formed. After that, an estimate of the object output with known values of the input variables is constructed based on the estimates of Nadarai-Watson. Thus, for given values of the input variables of such a process, it is proposed to carry out a procedure for evaluating the forecast of output variables in accordance with the developed algorithmic chain. Numerous computational experiments, studying the proposed models of partially-parameterized discrete-continuous processes have shown their rather high efficiency. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology for predicting values of output variables from known input variables.
Keywords: partially parameterized discrete-continuous process, identification, nonparametric estimates, КTmodels.
References

1. Medvedev A. V. Osnovy teorii neparametricheskikh sistem. Identifikatsiya, upravlenie, prinyatie
resheniy
[Fundamentals of the theory of nonparametric systems. Identification, management, decision making].
Krasnoyarsk, Reshetnev University Publ., 2018, 732 p.
2. Agafonov E. D., Medvedev A. V., Orlovskaya N. F., Sinyuta V. R., Yareshchenko D. I.
Prognoznaya model'
protsessa kataliticheskoy gidrodeparafinizatsii v usloviyakh nedostatka apriornykh svedeniy
[Predictive model of
the process of catalytic hydrodewaxing in the absence of a priori information]. Tula, TulGU Publ., 2018, No. 9,
P. 456–468 (In Russ.).
3. Medvedev A. V., Yareshchenko D. I. [About modeling of process of acquisition of knowledge by students
at University].
Vysshee obrazovanie segodnya. 2017, No. 1, P. 7–10 (In Russ.).
4. Medvedev A. V., Yareshchenko D. I. [On nonparametric identification of T-processes].
Siberian Journal of Science and Technology. 2018, Vol. 19, No. 1, P. 37–44 (In Russ.).
5. Nadaraya E. A.
Neparametricheskoe ocenivanie plotnosti veroyatnostej 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. Ehjkhoff P.
Osnovy identifikacii sistem upravleniya [Basics of identification of control systems]. Moscow, Mir Publ., 1975, 7 p.
8. Cypkin Ya. Z.,
Osnovy informacionnoy teorii identifikacii [Fundamentals of information theory of identification]. Moscow, Nauka Publ., 1984, 320 p.
9. Medvedev A. V.
Teoriya neparametricheskih sistem. Upravlenie 1 [The theory of non-parametric systems]. Vestnik SibGAU. 2010, No. 4 (30), P. 4–9 (In Russ.).
10. Medvedev A. V.
Neparametricheskie sistemy adaptacii [Nonparametric adaptation systems]. Novosibirsk, Nauka Publ., 1983, P. 173.
11. Cypkin Y. Z.
Adaptaciya i obuchenie v avtomaticheskih sistemah [Adaptation and training in automatic systems]. Moscow, Nauka Publ., 1968, 400 p.
12. Fel'dbaum A. A.
Osnovy teorii optimal'nyh avtomaticheskih system [Fundamentals of the theory of optimal automatic systems]. Moscow, Fizmatgiz Publ., 1963, P. 552.
13. Amosov N. M.
Modelirovanie slozhnyh system [Modeling of complex systems]. Kiev, Naukova dumka
Publ., 1968, 81 p.
14. Sovetov B. Ya., YAkovlev S. A.
Modelirovanie sistem: uchebnik dlya vuzov [Modeling of systems].
Moscow, Vysshaya shkola, 2001, 343 р.
15. Antomonov Y. G., Harlamov V. I.
Kibernetika i zhizn' [Cybernetics and life]. Moscow, Sov. Rossiya
Publ., 1968, 327 p.
  


Yareshchenko Darya Igorevna – senior lecturer of the department Intelligent Control Systems, Siberian Federal
University, Institute of Space and Information Technologies. E-mail: YareshenkoDI@yandex.ru.
  


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