SCIENTIFIC ABSTRACT KIRILLOVA, F.M. - KIRILLOVA, I.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000722710004-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 14, 2000
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

On the problem of the existence... S/140/61/000/002/002/009
CM/C222
where M a max lb ii (t)j 9 t010 i~ t; .
Lemma 1.21 If u(k (t) is a ainimizing sequence of (1.1) then the
sequence x(z t P )(t),t) contains at least one uniformly convergent
O~ko~(t) . X(x (kl)(t)~t). t
subsequence x 1 o,t0 u a e, to+T.
Lot d'rz p(k)(t)'
7t- 0 6 x+B(t) gu(t)+G( &x, t), k.0,1? ... (1-3)
be the equation of the disturbed motion for (1.1) for a variation of
the controlSu(t) and let
d,S x.p(k~(t) Sx+B(t) Su(t), k-0,1,~*~ (1-4)
4r
be the linear approximation of (1 -3) - If ;U(t) - Su (k)(t) then for
4~' (k)(t) anj S t(k)(t)
the corresponding solutions 6 x of 0.3) and (1-4)
it holdes
Lemma 1-3t The solutions of the systems (1-3) and (1-4) satisfy the
inequality
~-' (k) (t) (k) (t)
Xi k~1,29-,
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On the problem of the existence... S114016i'lOOOI00210021009
ClIlIC222
where 06t A 1c,
rr
S 16(k) (t) Idt and 0 for
t 0
Then the author considers the equation
ftW . p(k)(t)X(t)+B(t)w(t)' k-Oplv.-, (2.1)
dt
where the elements of the matrix P(k)(t) are equal to the functions
bfi (k)(t)
- calculated along the curves x (X(k)(t).#Xo(t) uniformly
;DXI
for k -W )- Lot B i(t) denote the J-th collm of B. Let P (t) be
the fundamental matrix of (2.1) for B(t)-30. Lot JktJB (t)]
(k)
donate the ocular product of the vector 1 and the vector F )Bj(t).
Tk) t
By use of oaxlier results of the author and others now the trajectories
Card 416

On the problem of the existence.- 3/140J61/000/002/002/009
C1111C222
of (2.1) are investigated in detail, The final result of these
investigations is contained in the
Theoremi If for the equation (1.A) the coordinato origin .'a reached
in the time T, for a control u 1)(t). and if the equations of the
linear approximation (1-4) satisfy the conditions
(1-[F-")(t)B (t)" A I, ~ 0, J- I - " -- 1, t
(k 0, (2.2)
2 nLT4
in the reKllon jr, (t) nr MET IQ i(U-MaA Jbij(t)j. t.,~.t,4to+j) then
there exists at least one optimal control b#ing a plecovise constant
function and determined by the formulas
uo(t) - N (t)'),
1 0 1 1
where the vector 1.0 to found from the condition
t +T
0 ,r,
min 4 (t)] )11t~
j t~-1 0
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On the problem of the existence-, 3/140/61/000/002/002/009
C111 C222
The author mentions L.s.rontryagin~ She thanke N.N.Krasovskiy for the
theme and the leading of the vork. There.are 11 Soviet-bloc references.
.LSSOCIATIONsUrallskiy politekhnichookly institut _1m-,S.X,KJrov& (U.-al
Po3ytechnical Institute im. S.M.Kirov)
SUBMITTEDs January 29, 1959
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26729
8/640/61/025/U03/006/026
21, 1344) D208/D304
AUTHOR: Kirillovap P.M. (Sverdlovsk)
TITLE: On the*problem of the analytic construction of
regulators
PERIODICAL: Akademiya nauk SSR. Otdeleniye tekhnicheskikh nauk.
Prikladnaya matematika i mekhanika, ve 25, noo 3.
19619 432 - 439
TEXT: The regulator system is written in the form
drk (1.1)
dt aArjxj 4- bkU (k
where xk are the phase coordinates, akj, b k are parameters, u is
the controlling influence produced in the regulator. In the matrix
form (1'1) is !L
x Ax + bu, At time t = Op x = x . The optimum cri-
dt 0
Card 1/7

On the problem of the
teria mE-,y be obtained from
J (11) 11 (u) dt,
26729
B/040/61/025/003/006/026
D208/D304
n (1.2)
(V (U) a4.rtl + C142
It is necessary to ex ress the controlt as a function of the coor-
dinates xlt toot xn# Ke question of the existence of a possible
control for the system (1.1 is considered, The function u(t) deno-
tes a possible control if uM satisfies the inequality J(u) --.+ Co.
If B is an n - n matrix and c an n-dimensional vector then (Bc)i
denotes the n-th component of their product. (a 0 b) denotes the
scalar product of vectors a and b. It is supposed that the vectors
bp Abp An-:Lb (2.1) are linearly independent. For a fixed point
xo there exists a number N(xoj t) such that
Min 1,2 + 0
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26729
5/040/61/025/003/006/026
On the problem of the D208/D304
where F(T) is the fundamental matrix of (1.1) with u _5 0. This im-
plies the existence of a control u(T) which, with the origin at
t
r 2 1 (0
~o
or the condition A2 1
J
ju t0 t j j -
The control term uo(t) is sought for.whioh the point x, moving on the
i
controlled trajectory of the systemq passes from the po tit X(t 2
0 0
I J.
Into,the origin in the shortest time T. The main content of the paper
consist in the proof of the theorem's If there exists an optimal controll
s(
term u0 t) under condition A there exists
2 t then,under,condition A,
a number pq such that the optimal control term u(pot) (for the problem
with, condition A) alao existo for p> yj where for p-tco it holds t
17V*
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foco
AUTHOR:,
TITLE;
PERIODICAL:
3P799
S/ 017/004/001/001
B112/B108
Kirillovi, F.
Continuous dependence of the solution to an optimum control
problem'on the initial data and parameters
Uopekhi matematichookikh nauk, v. 17, no. 4 (106), 1962,
141-146
TEXT: The author considers a control problem vhich is describeS by the
equation dx/dt -. f(x,t 4) + B(tlA)u(t)s where x is a vector in ieal
n-~dimsnoional space X,, 4 is a numerical parameter (AA- A), B(t, A)- (b ik(tlh)J
(1 0 1,,..e,ni k-l,**,,r) is a matrix, u(t) is a piecewise continuous*
controlling influence satisfying the conditions (k.1, ... r).
luk(t)l 4 1
It is assumed that A is an open set B is continuous on txA, the funotion~
f(x,t,,x-) - (fj(xjt1X)j9**9f and its Partial derivatives Wax
n j
(J- 19 gn) are continuous on X x t v A9 f fulf ills Ltpachitz conditions in
X uniformly with respect to X, and f(Ojt9h) - 0. It is demonstrated that
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5/042j62/017/004/001/001
Continuous d.opendence of tho..~. B112/B108
the minimum time T(x tt $A) for--Ivfiioh X(x 't qAjTju(T)) 0 depends
0 0 0 0
continuously'on z and A.
0
SUBMITTED: July 27o 1959
Card 2/2

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GABASOV., R.; KIRILLOVA, F. M. ( Sverdlovsk)
"Application of the theory of linear inequalities to optimal
control problems"
report presented at the 2nd All-Union Congress on TheoreticaIL and Applied
Mechanics., Moscow,, 29 Jan - 5 Feb 1964.

ACCESSION NR: AP4015301 S/0280/64/000/001/0132/0142
AUTHOR, Gabasov, R. (Sverdlovsk); Kirillova, F. M. (Sverdlovsk)
TITLE: Problems of optimum control
SOURCE: AN SSSR. Izvostiya. Tekhnichoskaya kibornatika, no. 1, 1964, 132-142
TOPIC TAGS: optimum automatic control, optimum automatic control theory,
controlling variable constraint, phase coordinate constraint, controllable order
automatic system
ABSTRACT; Optimum processes are theoretically oxan-dned In coupled
automatic -control systoms which have a controlling -variable constraint and a
phase -coordinate constraint in one of the component systems at predetermined
moments of time. Systems are studied that contain. in addition to ordinary
controls, iree parameters In their right-hand members,, the parameters can be
selected at specified moments of time. By using the L-problem results, this
form of the optimum control for a two-plant couplod automatic system (sea Fig 1,
Enclosure 1) has been developed%
Card I

ACCESSION NR: MOM* 8/01"/64/006/001/00N100W
AUTHOR: Kirilloya, M.
TITLE: The problem of the existence of an q*num control fummon for a linear systm
with random perturbatiou
~SOURCE: Sibirsidy matematichesidy zhurnal, Y. So no. 11 19649 66-93
iOPIC TAGS: -automation, control system, optimum control, linear system optimum
control, Markov process
ABSTRACT: A generalization of the Itnown opUmwn control problem discussed by
R. Bellman, J. Glicksberg and 0. Gross (Quart. Appl. Math. j 14, No. 1 (1956) 11-18) X
and other Soviet and Western authors is presented. The approach differs from ihe usual
in that an optimum control action is sought rather than a choice of an optimum operator.
Let there be given a linear system which is acted upon periodically by a random pertur-
bation whose distribution obeys the laws of a Markoy process. The main result of the
,-paper is to demonstrate that a damping of the system exists such that the expected kicii-_ -e
tage of the time that the system shall be "distant" from the rest state shall be a minimum.
More exactly, let tbere be given a system of dWerential equations
Ai +-bu
Card 1/3 di.

ACCESSION NR: AP4012346
where x (xj, x2, x n) is the representation vector in the phase space X, b - (bi,
bn), c I (01t ... 9 on) are constant (real) vectors A - (aij) in any matrix of order n, and
U(t) Isa pleoewise continuous "control factor: BaNwnir.
(2)
It is assumed that b, Ab, An-lb am Unearly independent and that the characteristic
roots of Pi of the matrix A satisfy
RePA