SCIENTIFIC ABSTRACT PUGACHEV, V. S. - PUGACHEVA, A. I.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001343530007-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 15, 2000
• Sequence Number: 7
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

USSR/Mathematics - Probability, SeP/Oct 53
Stochastic Functions
"General Theory of the Correlation of Stochastic
Functions,"JV. S. Pugachev-
Iz Ak Nauk SSSR, Ser Mat, Vol 17, No 5, pp 401-420
~he author expounds certain general results of the
methods for investigating stochastic functions,
which he developed in 1947-1948 ("Fundamentals
of the General Theory of Chance Functions," T!rudy
Akademii Art. Nauk (Works of the Academy of
Artillery Sciences], 1952). Having in mind the
creation of an applied theory sufficiently simple
274T68
and convenient in practical applications, the
author limits himself mainly to a study of those
propertii~s of stochastic functions which are
characterized by.moments; of the first and second
order - the mathematical expectations and the
correlational functions. Presented by Acad"A. X.
Kolmogorov, 6 Jan 53.

124-58-b-6330
Translation from: Referativnyy zhurnal, Mekhdnika, 1958, Nr 6, p 7 ("-,'SSR)
AUTHOR- Pugachev, V. S.
T IT LE: The General Theory of Random Functions and its Application to
tht Theorv oi Automatic Control (Obshchaya teoriya stuchAynykh
tunktsly I yeye pr'menenlye v !eorii avtomdticheskogo regutiro-
k"niya)
PERIODICAL: Tr. 2-go Vses. sove--lichaniya po teorii avtomaticheskogo
regul; rovaniyd. Vol 2. Moscow-Leningrad Izd-vo AN SSSR,
1955, pp 403-4,,4
ABSTRACT: This survey, founded mainly on material from previous
writings of the author (Izv. AN SSSR. Ser. matem. . 1953, Vol
17, Nr 5, pp 401-420, et al. ), touches upon many of the points
covered in his subsequent monograph (Teoriya sluchaynykh
funktsiy i yeye primeneniye k zadacham avtomaticheskogo uprav-
leniya [Theory of Random Functions and its Application to the
Problems of Automatic Control ] . Moscow, Gostekhizdat, 1957).
The survey contains the following sections: 1) the moments of
random functions (determination and characteristic properties
Card 1/3 of the moments of different orders, the steady state in the

124-58-6-6330
The General Theory of Random Functions and its Application (cont. )
narrow and broad sense); 2) the theory of canonical expansions of random
functions (the different forms of canonical expansions, including spectrum
analysis in the case of stationary functions); 3) vectorial random functions
(determination and canonical expansion of such functions), 4) the theory of
the linear transformations of random functions (formulae for their moments,
also canonical expansions of a random function obtained from an initial ran-
dom function with known moments and known canonical expansions by means
of a linear transformation); 5) the theory of nonlinear transformations of
random functions (data concerning the moments and canonical expansions of
a random function obta-ined with the aid of a nonlinear transformation);
6) a statistical investigation of random systems (application of the theory of
linear transformations of random functions to the linear transformations
achieved with linear automatic -control systems) 7) approximate statistical
Investigation of nonlinear systems by means of t~e linearization method
(application of the method of canonical expansions to systerrLs described by
nonlinear equations, with subsequent linearization) 8) a statistical inves-
tigation of nonlinear systems (application of the methods of Section 5 to
nonlinear automatic -control systems) 9) des ign- engineering problems in
automdtic -control system desion (a short survey of the work that has been
dcne in this field) 10) outlook for the development of statistical methods in
Card 2/3

124-58-6-6330
The General Theory ot Rardorn Functions and its Applic~rion (ccn% )
the theory of automatic control (an enumeration of problems requ:Lring further
development). Bihliography: 17 references
A. M. Yaglcm
1. Control systems--Automation
Random -'unctions--Theory
3. Mathematics--Applications
Card 3/3

PUGACHEV, (Prof-Eng. D Major Oeneral) and WISOV) V. (Lecturer,Bach. Tech. Sci.,Engr.)
"Guided Missiles,," Krasnaya Ivezda, later reprinted in Skrzydlata Polska
(Winged Poland), No.17, pp 8 and 9, 1955
Translation of an extensive summary D 311976, 1 Sep 55
The authors describe various kinds of guided missiles, but fail to
supply any details or data. Anti-aircraft guided missiles are bmztn briefly mentioned
and there is no word about two-stage missiles or air-to-air missiles. No particular
missile is specified except the B-61 "Matadoru.

"all NR:
Transactions of the Third All-union MathemaLical Congress, Moscow, Jun-Jul 50,
Trudy '56, V. 1, Sect. Rpts., Izdatel'stvo AN SSSR, Moscow, 1956, 237 pp-
Pugachev V S (Moscow). On the Transformation of
Entropy of Random Function During the Linear Transformation
of Random Functions. 125-127

"Condition and Prollems of Development of ?andom Functions and Probabilit'r Net~-Iods
of the Theor-,- of Automatic Control,"
paper repd at the Session of the Acad. Sci. USSH,on Scientific eroblems of Automatic
Production, 11 -'-20 Octo'--cr 1956.
Avtomatika i telemekllranika, No. 2, p. 182-192, 11057.
9015229

17 - - ;c
and ?~2'lhodz~ of Applicatior. Of Guidee I-lissiles", from tile book,
-n ?Iilitar- T--2chnoiogy, 1956, page 26
11"'de. .. 11
Trwisl-atici-, 111hrfr,

F
geneial conditfou f6r, ml~zllivi
mean s re
pr a dynam!cW systeni. A W t
Te SH -
"A Itnielh. 17, ~(I, 289-295; appendix to no'. 4, 1 2
in.:, En&h sat-6mary)
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IT
f Y(i);' (t' he ~'signal"), 4nd X').' (the "noise - are
-stutable c.oniolex-valkd kesses, and, R Al
stochastic pr( J-
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selVa rriaybeiiouhnearb ~ necessary and suffident con-,
aie-of -Y(z) is.
tl -AX(l)-be a least-S
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])=~b -ail B c-R
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by means aniily~of random yanables':
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,beise 'results generalize earlier resulO

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:by the author [Sb.,Nauftyh- Trddov V
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USSR/Genera- Sec'Qi~)n
Abs Jour Referat Zhur Pizikal No 5, 1957, No 10784
Author PUgachev,V.S.
Inst Not given
Title Application of Canonical Expansions of Random Functions
to the Determination of the Optimum Linear System.
Orig Pub kvtomatika i Telemekhanika, 119,56, 17, No 6, 489-499
A
Abstract The author treats a generalization of the theory of canoni-
cal expansion of random functions, previously developed by
him, and the application of the theory of canonical expan-
sions for the finding of a generai solution of an equation
that determines an optimum linear dynamic system, using the
condition of minimum rms error.
Card 1/-,

PUGACHEV, V.S. (Moskva)
~Po=viblMgenmral solution for problems on determining optimum
dynamical systems. Avtom. i. telem. 17 no-7:585-589 JI '56.
(MLRA 9,.10)
(Mathematical physics) (Mechanics, Analytic)

Call Nr: QA273.P83
AUTHOR: Pugachev, V.S.
.,TITLE: Theory of Random Functions and Its Application to the
Problems of Automatic Control. (Teoriya sluchaynykh
funktsiy i rimeneniye k zadacham avtomaticheskogo
upravlenjya~eye p
PUB. DATA; GoBudarstvennoye izdatel'stvo tekhniko-teoreticheskoy
literatury, Moscow, 1957, 659 pp., 8000 copies
ORIG. AGENCY: None given
EDITOR: Sobolev, 0. K.; Tech. Ed.: Gavrilov, S. S.
PURPOSE: The book is intended for scientists and engineers deal-
ing with automatic controls and with the automatization
of various branches of production.
COVERAGE: The monograph is a systematic presentation of the applied
theory of random functions and of probability methods of
the theory of automatic control. The author thanks
Andreyev, N.I., Merkulova, Ye.P., Sedov, V.D., Sobolev,O.K.
Card 1/2# and Pugacheva, I.V. The book deals with Russian

Call Nr: W7~ - P83
Theory of Random Functions and Its Application to the Problems tCont.
contributions. There are 56 references, 44 of which are USSR,
7 English, 2 German, I French, and 2 translations into Russian.
TABLE OF CONTENTS
Foreword 9-11L
Ch. 1. Probability of Events and the Properties of
of-Probability. 15-29
1. Random phenomena. Subject of the theory of
probabilities. 15-19
2. Experimental foundations of the theory of probabilities.
Frequency and probability of events. 19-22
3. Addition theorem of frequencies, Principle of addition
law of probability. 22-24
Card 2/26

AUTPOR DOSTUPOV, B.G., M&QHLN'_Y'rL_(MosCow)
TITIZ The Equation to Define a Probability Distribution, of the Integral of a
System of Ordinary Differential Equatiorswith Random Parameters
(Uravnenly*, 9predelyayushcheye %akon ramprodeloniya integrala sistemy
obyknovennykh differentsiallnykh arsvnenly, Russian)
PERIODICAL Avtomatika i Tolemakhanika, 1957, Vol 18, Nr 7. pp 62o - 63o (U.S.S.R.)
ABSTRACT A general equation is derived, which determines the probability densf:ty
of the integral of ordinary differential equations which'contain random
parameters. A possible method for an approximated integration of this
equation is shown. This method is useful for computation on calculating
machines. After determination of the integral-distribution'law, a12 no-
cossary integral, moments, and aspecialLy their mathematical expectation
as well as the correlation matrix can be determined -according to the
ordinary formula* of the probability theory. The method given here ma *
also be applied for differential equations which contain random functions
For this purpose all random functions contained in the equations are to
be approximated by finite sections of the canonical disintegration. The
method in applicable to any system of ordinary differential equations
under the following condition, - all, functions containd in the equations
are steady with respect to unknown functions and occasionally have steady
derivations towards all unknown functions. In consideration of the com-
Card 1/2 plication of the necessary computations, the method given her* at present

105 -7 -V11
AStOCIATION
PRESENTED BY
SUBMITTED
AVAILA,BLE
The Equation to Define a Probability Distribution, of the Integral ~,f 2
System of Ordinary Differential Equations with Random Parameters
is mainly of theoretical value as a means of a possible initial pcint
for working out now methods of a statistical analysis of non-linear
systems. (With 15 Slavic references).
Not given
20.9-1956
Library of Congress
Card 2/2

Tl;,_'~'. PuCachev. V.
(11.10scow) 103-11-3/10
A Canonical Representation of Random Functions by Integrals
and their Application for the Determination of Optimum Linear
Systems (Integrallnyye kanonicheskiye predstavleniya sluchaynykh
funktsiy i il:h primeneniye k opredeleniyu oDtimallnykh lineynykh
sistem).
---.___~DICAL: Avtomatik-- i Telemekhanika, 1957, Vol. -984
.L(- 18, Nr 11, PP. 971
(USSR)
~.:~32RACT: The problem of the canonical reDresentation of random functions
consists in finding the expression of any random function of the
simplest type, viz. a random function the values of which at
different azgument-values are not in correlation with one another.
This random function with a mathematical zero-expectation and
values which are not in correlation is called "white noise"
irrespective of the nature of its argument. The theory of the
canonical representation of random functions by integrals and
their application for the determination of optimum linear opec-
ators is here dealt with. A formula for the function of the weight
of an optimum one-dimensional linear system is deri-~red for the
case of an infinite observation integral (infinite system
ca!-! 112 memory), where the observed random function is a result of the

7-an-nical Repre3entation of Random Functions by Integrals 103-11-3110
t.1-,iT Application for the Determination of Optimum Linear Systems.
passage of the "white noise" through a eertain linear system.
In s5ecial cases the well-known formulae by N..Wiener (New York
1949 and R. C. Booton (Proc.IRE, Vol. Ao, Nr , 1952) are ob-
tained from the formula mentioned here. There are 6 Slavic
references.
S 1B TTED. "larch 11, 1957
Library of Congress

"New Methcds c;-f Detec-ting and Repruducing Sig als 'r Presence c--:'
gn
Interferences."
scientf-fic report oresented at the Pleriary Meetliig (A.' the Depirtmnet (-f
Engineering Sciences, Acad. Sci. USSF, 1~~ ~-17 June 1958.
(VesL. AN SSSSR, 1958, No. S, pp. 57-68)

AUTHOR: Puaacliev, V.S. (Moscow) lo3-19-6-2/'13
TITLE: Dei'ern the Optimum System According to kny Criterion
(O.predeleniye optimallnoy sistemy po proizvollnomu kriteriyu)
PERIODICAL: Avtomatika i telemekhanika, 1958, Vol 19,. Nr 6,
PP 519 - 539 (USSR)
ABSTRACT: The present paper gives a method for determining the optimum
operator A according to any criterion of the Bayes type (or
a conditional Bayes criterion) according to formula (1) for
the case where the observed accidental function Z and the signal
W to be reDroduced are expressed bjr the formulae (3) and (4).
In this connection it is assumed that the accidental vector-
-functionCX(t), Y(s)j is normally distributed and statistically
independent of the accidental vector (Ul, ... ) U U). On that
occasion it can be assumed without loss of generality, that the
mathematical expectations of the accidental functions X and Y
identically equal zero (References 1,2). The arguments t and s of
the accidental functions are assumed as any scalar or vector
variables which may in special cases possess several discreet
Card 1/2 components. Therefore the theory here given may be applied to

Determination of the Optimum System According to Any 103-19-6-2/13
Criterion
scalar as well as to vector functions. In order to be able to
use them in vector functions, it is sufficient to consider
the component of every vector function as a scalar function of
its --juments and the number. In this manner the method here
given may be used for determining the optimum system in unidi-
mensional as well as jr; multidimensionil systems. As formula (5)
shows it is sufficient for the solution of tile problem posed to
find a certain operator. A which guarantees the minimum of the
conditional mathematical expectation of the function r with re-
gard to the observed accidental function Z for every possible
realization of the accidental function Z (except some realiza-
tions with a zero-sum of the probability of occurrence) ...
formula(6). The problem posed 'nere is solved in a general form
according to the method of the canonical decomposition of acci-
dental functions. This method yields a sufficiently simple
algorithm for finding the optimum operator. There are 6 references,
5 of which are Soviet.
SUBMITTED: December 16, 1057
Card 2/2 1, Servomechanisms--Mathematical analysis

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PUGACHEV, V.S. (Moskva)
Solution of the basic integral equation of the statistic theor7
of optimum systems in the finite form. Prikl. Mat. i mekh- 23
n0-1:3-14 Ja-F 159. (MIRA 12:2)
(Integral equations)

PUGACHEV, V.S. (Moskva)
Method for determining eigenvaluea and eigenfunctions for a certain
class of linear integral equations. Prikl. mat. i mekh. 2.3 no-3:
527-533 MY-Je '59. (mM 12:5)
(Integral equations) (Iligenvalues) (ligonfunctions)

I hOJK -PLOITATION X7/1,/,78
,T~~chev~, Vladimir Semenovich
Teoriya sluchaynykh funktsiy i yeye primeneniye k zadacham avtomaticheskogo
upravleniya. (Theory of Random Functions and Its Application to Problems of
Automatic Control) 2nd ed., rev. and enl. Moscow, Fizmatgiz, 1960. 883 P.
10,1~.O copies printed.
'11~; O.K. Sobolev; Tech. Ed.: N.Ya. Murashova.
"POSE-. This book is intended for
automatic control and automation
,lineering. It may also be useful
technical fields involving problems
,Iseful information as well as noise
scientists and
of production
to specialists
of transformation
or interference.
COVERUGE: The book systematically presents the
and also stochastic methods of the theory of
nqmics of automatic control systems). After
the law of probability, the fundamental cone
are considered. A presentation of the gener
Methods for investigating the exactness of 1
Ga.r~," 6
working in the field
branches of en-
engineering and other
signals which contain
applied theory of random functions
automatic control (statistical dy-
a brief treatment of the basis of
pts of the theory of random functions
1 theory of linear systems is given.
near and nonlinear systems are con-
engineers
in various
in radio
of

')00 4- 66we 69 ( , 1(3
1
c S/021+/60/000/02/012/031
R140/Z135
AUTHOR; - Pugachev, V.S. (Moscow)
TITLE; Met~od"for Determining Optimal System According to the
General Bayes' Criterion
PERIODICAL: Izvestiya Akademii nauk SSSR, Otdeleniye tekhnicheskikh
nauk, Knergetika i avtomatika, 196o,Nr 2, pp 83-97 (USSR)
ABSTRACT: This paper was presented on January 10, 1959 at the
Seminar on Probability Methods in the Theory of Automatic
Control at the Institute of Automation and Remote Control,
Academy of Sciences USSR. The method was also described
in a paper presented at the Second Prague conference on
the theory of information, statistical solutions and
random processes. A, method is presented for
determining the optimum system from the general Bayes'
criterion when the observed function and the signal to be
detected or reproduced depend on a finite-dimensional
random vector U with additive noise, with distribution
normal and independent of the vector U. In certain cases
Card the vector U has an infinite (denumerable) set of
1/~�- components. A special case is the previously published
(Ref 1) method for linear dependence of the observed

4"IR (996Y3
S/024/60/000/02/012/031
EJI+O/El35
Method for Determining Optimal System According to the General
Bayes' Criterion
function on the vector U. The method is also applicable
to cases where the observed function may be reduced to the
sum of a certain function of the vector U and the
independent normally distributed noise by a non-linear
transformation independent of the vector U.
1. Statement of the problem. The general problem of
determining optimal systems intended for detectiorj,