З.Г. Широкова, Аунг Чжо Со, А.М. Макаренков
12
Analysis and identification of one class of systems with
distributed random parameters
© Z.G. Shirokova, Aung Kyaw Soe, A.M. Makarenkov
Kaluga Branch of Bauman Moscow State Technical University, Kaluga, 248000, Russia
Control of distributed systems is a complex problem that requires the construction of
adequate mathematical models, including models, which take into account the effects of
random factors. This article describes the method of statistical analysis of systems with
distributed parameters in the Goursat problem statement and the method of parametric
identification in the context of the definitions of the statistical characteristics of random
parameters of these systems. Both methods are based on the use of the so-called projec-
tion models, which are the result of a projection approximation of the original continu-
ous models, described by partial differential equations with random coefficients. This
approximation is performed using the operational matrices. The key point is the analyti-
cal procedure of averaging stochastic system operator based on the approximate repre-
sentation of that operator in the form of the matrix series. In result the averaged projec-
tion model of system with distributed random parameters is obtained. The problem of
identification of unknown statistical characteristics of the random parameters of the
mathematical model is reduced to the minimization of a quadratic functional, calculated
using the averaged projection model. Example of solving the problem of identification of
mean value and variance of a random parameter of stochastic system is considered. Us-
ing the averaged projection models allows building effective computational algorithms
for solving problems of statistical analysis and parametric identification. These algo-
rithms are suitable for parallel implementation.
Keywords:
distributed parameters, statistical analysis, random parameters, stochastic
system, identification, mathematical model, projective approximation, matrix operator.
REFERENCES
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Uravneniya matematicheskoy fiziki
[Equations
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Pupkov K.A., Egupov N.D., Makarenkov A.M., Trofimov A.I.
Teoriya i
kompyuternye metody issledovaniya stokhasticheskikh system
[Theory and
Computer Methods of Study of Stochastic Systems]. Moscow, Fizmatlit, 2003,
400 p.
Shirokova Z.G.
(b. 1971) graduated from Kaluga branch of Bauman Moscow State
Technical University in 1996. Ph.D., Assoc. Professor of the Department of Electrical
Engineering at the Kaluga branch of Bauman MSTU. She is the author and co-author of
more than 40 publications in the field of application of projection methods for research of
systems with random parameters. e-mail:
Aung Kyaw Soe
received a master's degree in Kaluga branch of Bauman Moscow State
Technical University in 2011. He is a graduate student of the Department of Automatic
Control Systems at Kaluga branch of Bauman MSTU. The area of his scientific interests
is application of projection methods for research of systems with random parameters.
е-mail:
Makarenkov A. M.
(b. 1961) graduated from Kaluga branch of Bauman Moscow Higher
Technical School in 1984. Ph.D., Assoc. Professor of the Department of Automatic Con-
trol Systems at the Kaluga branch of Bauman MSTU. He is the author and co-author of
more than 120 publications and one monograph in the field of application of projection
methods for research of systems with random parameters. e-mail:
