UDK 004.942 Doi: 10.31772/2587-6066-2018-19-3-452-461
ON NONPARAMETRIC MODELING SPINNING SYSTEMS WITH DELAY
A. V. Tereshina, D. I. Yareshchenko*
Siberian Federal University, 26/1, Kirensky Str., Krasnoyarsk, 660074, Russian Federation. *E-mail: YareshenkoDI@yandex.ru
This article is devoted to the construction of a new class of models under incomplete information. In this article we will discuss multidimensional inertial-free objects, where the output vector components are stochastically dependent, but the nature of this dependence is not known to us. Constructing a model of a multidimensional inertial-free object, when the input and output vectors are not linear, leads to the necessity to solve the problems of systems of implicit functions. It should also be noted that the form of these functions is unknown up to parameters. So there is a need to use T-processes, when predicting output variables is carried out by known input. Thus there is a system of nonlinear im plicit equations which form is unknown at the initial stage of the statement of the identification problem, but it is only known that this or that component of the output depends on other variables that determines the state of the object. Proceeding from the above, a nontrivial situation arises that solves a system of implicit nonlinear equations under the conditions when the equations themselves are not in the usual sense. Consequently, the model of the object can not be constructed using the existing theory of identification because of the lack of a priori information. Therefore, the solution of this system can be represented in the form of some successive algorithmic chain of the T-model. The main goal of this paper is to solve the identification problem for multidimensional inertia-free objects with delay, in the presence of T-processes, i.e. construction of T-models under conditions of nonparametric uncertainty. In this case, to predict the output variables by the known input, it becomes necessary to use a step-by-step solution of the problem under consideration. In the article some calculations of the T-process simulation will be presented, which showed the high efficiency of the proposed technology of forecasting the values of the output variables by the known input. Keywords: identification, mathematical modeling, T-models, T-processes.
Keywords: identification, mathematical modeling, T-models, T-processes.
References

1. Medvedev A. V. Neparametricheskie sistemy adaptacii [Nonparametric adaptation systems]. Novosibirsk, Nauka Publ., 1983, 174 р.

2. Dub Dzh. L. Veroyatnostnye processy [Probabilistic processes]. Moscow, Iz-vo inostrannoy literatury Publ., 1956, 605 p.

3. Medvedev A. V. Osnovy teorii adaptivnyh system: monografiya [Fundamentals of adaptive systems theory]. Krasnoyarsk, SibGAU Publ., 2015, 526 p.

4. Medvedev A. V. Osnovy teorii neparametricheskih sistem. Identifikaciya, upravlenie, prinyatie reshenij [Fundamentals of the theory of nonparametric systems. Identification, management, decision making]. Krasnoyarsk, SibGAU Publ., 2018, 732 p.

5. Ehjkhoff P. Osnovy identifikacii system upravleniya [Fundamentals of identification of control systems]. Moscow, Mir Publ., 1975, 681 p.

6. Ehjkhoff P., Vanechek A., Savaragi E., Soehda T., Nakamizo T., Akaike H., Rajbman N., Peterka V. Sovremennye metody identifikacii system [Modern methods of system identification]. Moscow, Mir Publ., 1983, 400 p.

7. Vasilev V. A. Neparametricheskoe ocenivanie funkcionalov ot raspredeleniy stacionarnyh posledovatelnostey [Nonparametric estimation of functionals of distributions of stationary sequences]. Moscow, Nauka Publ., 2004, 508 p.

8. Lyung L. Identifikaciya system [Identification of systems]. Moscow, Nauka Publ., 1991, 432 p.

9. Cypkin Y. Z., Osnovy informacionnoy teorii identifikacii [Fundamentals of Information theory of identification]. Nauka Publ., 1984, 320 p.

10. Amosov N. M. Modelirovanie slozhnyh sistem [Modeling of complex systems]. Kiev, Naukova dumka Publ., 1968, 81 p.

11. Medvedev A. V. Teoriya neparametricheskih sistem. Upravlenie 1 [The theory of nonparametric systems. Management 1]. Vestnik SibGAU. 2010, No. 4 (30), P. 4–9 (In Russ.).

12. Pupkova K. A., Egupova N. D. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 1: Matematicheskie modeli, dinamicheskie harakteristikii analiz sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control. Vol. 1: Mathematical models, dynamic characteristics and analysis of automatic control systems]. Moscow, Iz-vo MGTU im. N. E. Baumana, 2004, 656 p.

13. Pupkova K. A., Egupova N. D. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 2: Statisticheskaya dinamika i identifikaciya sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control. Vol. 2: Statistical dynamics and identification of automatic control systems]. Moscow, Iz-vo MGTU im. N. E. Baumana, 2004, 640 p.

14. Pupkova K. A., Egupova N. D. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 4: Teoriya optimizacii sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control. Vol. 4: Theory of optimization of automatic control systems]. Moscow, Iz-vo MGTU im. N. E. Baumana, 2004, 744 p.

15. Yareshchenko D. I. O neparametricheskoy identifikacii T-processov [On nonparametric identification of T-processes]. Siberian Journal of Science and Technology. 2018, Vol. 1, No. 1, P. 37–44 (In Russ.).


Tereshina Alina Vitalievna – Master’s Degree student, Department of Intellectual Control Systems, Institute of Space and Information Technologies, Siberian Federal University. E-mail: tereali09@mail.ru.

Yareshenko Darya Igorevna – senior teacher, Department of Intelligent Control Systems, Institute of Space and Information Technologies, Siberian Federal University. E-mail: YareshenkoDI@yandex.ru.


  ON NONPARAMETRIC MODELING SPINNING SYSTEMS WITH DELAY