Сибирский журнал науки и технологий
ISSN 2587-6066

Vestnik sibsau
Vestnik sibsau
Vestnik sibsau
Vestnik sibsau

UDK 52-601 Doi: 10.31772/2587-6066-2018-19-3-405-411
TO NONPARAMETRIC IDENTIFICATION OF DYNAMIC SYSTEMS UNDER NORMAL OPERATION
M. E. Kornet, A. V. Shishkina*
Siberian Federal University, Space and Information Technology Institute, 26b, Kirensky Str., Krasnoyarsk, 660074, Russian Federation. *E-mail: nastya.shishkina9666@mail.ru
The problem of nonparametric identification of linear dynamic objects is being investigated. In contrast with parametric identification, the case is analyzed when equations describing a dynamic object are not specified according to the parameters. Moreover, the identification problem is analyzed under normal object operation, opposite to the previously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is inputted to the object during normal operation and weight function realizations are represented by observations of input-output object variables measured with random interferences. As a result, we have a sample of input-output variables. As linear dynamical system can be described by the Duhamel integral, with known input and output object variables, corresponding values of the weight function can be found. This is achieved by discrete representation of the latter. Having such realization, nonparametric estimate of the weight function in the form of the nonparametric Nadaraya–Watson estimate is used later. Substituting this into the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of nonparametric model constructing when a delta-shaped function is inputted to the object. It was interesting to find out how delta-shaped function might differ from the delta function. The weight function was determined in the class of nonparametric Nadaraya–Watson estimates. Nonparametric models were investigated by means of statistical modeling. In general, nonparametric models have shown sufficient efficiency in terms of accuracy prediction by nonparametric model in relation to the actually measured output of the object. Evidentally, the accuracy of nonparametric models reduces with the growing influence of interference from the measurement of input-output variables or the discreteness of their measurement. Previously proposed nonparametric algorithms consider the case when Heaviside function was applied to the object, which narrows the scope of nonparametric identification practical use. It is important to construct nonparametric model of a dynamic object in conditions of normal operation.
Keywords: duhamel integral, transient function, weight function, delta-shaped input, Nadarya–Watson estimate, nonparametric model.
References

1. Tsypkin Ya. Z. Informatsionnaya teoriya identifikatsii [Information theory of identification]. Moscow, Nauka, Fizmatlit Publ., 1995, 336 p.

2. Raibman N. N. Chto takoe identifikatsiya [What is identification]. Moscow, Nauka Publ., 1970, 119 p.

3. Eykhoff P. Osnovy identifikatsii sistem upravleniya [Fundamentals of identification of control systems]. Moscow, Mir Publ., 1975, 681 p.

4. Medvedev A. V. Neparametricheskie sistemy adaptatsii [Nonparametric adaptation systems]. Novosibirsk, Nauka Publ., 1983, 174 p.

5. Medvedev A. V. [Adaptation under conditions of non-parametric uncertainty]. Adaptivnye sistemy i ikh prilozheniya [Adaptive systems and their applications]. Novosibirsk, Nauka Publ., 1978, P. 4–34.

6. Medvedev A. V. [The theory of nonparametric systems. Modeling]. Vestnik SibGAU. 2010, No. 4 (30), P. 4–10 (In Russ.).

7. Medvedev A. V. Elementy teorii neparametricheskikh sistem upravleniya. Aktual'nye problemy informatiki, prikladnoy matematiki i mekhaniki. Informatika [Elements of the theory of nonparametric control systems. Actual problems of computer science, applied mathematics and mechanics. Informatics]. Novosibirsk, Krasnoyarsk, Izd-vo Sib. otd-niya Ros. akad. Nauk Publ., 1996, P. 87–112.

8. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 1: Matematicheskie modeli, dinamicheskie kharakteristiki i analiz sistem upravleniya [Methods of classical and modern theory of automatic control. Vol. 1: Mathematical models, dynamic characteristics and analysis of control systems]. Ed. K. A. Pupkova, N. D. Egupova. Moscow, MSTU im. N. E. Bauman Publ., 2004, 656 p.

9. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 2: Statisticheskaya dinamika i identifikatsiya sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control. Vol. 2: Statistical dynamics and identification of automatic control systems]. Ed. K. A. Pupkova, N. D. Egupova. Moscow, MSTU im. N. E. Bauman Publ., 2004, 640 p.

10. Nadaraya E. A. Neparametricheskoe otsenivanie plotnosti veroyatnostey i krivoy regressii [Nonparametric estimation of the probability density and the regression curve]. Tbilisi, Izd. Tbil. University Publ., 1983, 194 p.

11. Kotkinik V. Ya. Neparametricheskaya identifikatsiya i sglazhivanie dannykh [Nonparametric identifica tion and data smoothing]. Moscow, Nauka Publ., 1985, 336 p.

12. Grop D. Metody identifikatsii system [Methods of identification of systems]. Ed. E. I. Krinetskiy, A. Vasilyev, V. I. Lopatin. Moscow, Mir Publ., 1979, 304 p.

13. Tse E., Bar-Shalom Y. An actively adaptive control for linear systems with random parameters via the dual control. Automatic Control, IEEE Trans. 2003, Vol. 18, Iss. 2, P. 109–117.

14. Wenk C. J., Bar-Shalom Y. A multiple model of an adaptive dual control algorithm for stochastic systems with unknown parameters. Automatic Control, IEEE Trans. 2003, Vol. 25, Iss. 4, P. 703–710.

15. Liung L. Identifikatsiya sistem [Identification of systems]. Moscow, Nauka Publ., 1991, 423 p.

16. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 3: Sintez regulyatorov sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control. Vol. 3: Synthesis of regulators of automatic control systems]. Ed. K. A. Pupkova, N. D. Egupova. Moscow, MSTU im. N. E. Bauman, 2004, 656 p.

17. Agafonov E. D., Shishkina A. V. [Nonparametric control of a dynamical system]. Siberian Journal of Science and Technology. 2017, Vol. 18, Iss. 4, P. 711–718.


Kornet Marya Evgenevna – applicant of Department of System and operation analysis, Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology. Е-mail: marya.kornet@gmail.com.

Shishkina Anastasia Vasiljevna – student, Institute of Space and Information Technologies, Siberian Federal University. E-mail: nastya.shishkina9666@mail.ru.


  TO NONPARAMETRIC IDENTIFICATION OF DYNAMIC SYSTEMS UNDER NORMAL OPERATION