RUu =∈ Rx ∈ Ry ∈ R U RT:f →× × R RT:g → ×

ɊȺɁȼɂɌɂȿ ɄɈɇɐȿɉɐɂɂ ȽɂȻɄɂɏ ɌɊȺȿɄɌɈɊɂɃ
ȼ ɁȺȾȺɑȺɏ ɌȿɊɆɂɇȺɅɖɇɈȽɈ ɍɉɊȺȼɅȿɇɂə
ɉɈȾȼɂɀɇɕɆɂ ɈȻɔȿɄɌȺɆɂ
ȿ.Ⱦ. Ɍɟɪɹɟɜ1, Ʉ.ȼ. ɉɟɬɪɢɧ1, Ⱥ.Ȼ. Ɏɢɥɢɦɨɧɨɜ1, ɇ.Ȼ. Ɏɢɥɢɦɨɧɨɜ2
1
$ # . &.&. ; %&'
101990, 2, 2
3 ., 4, %
[email protected]
: +7 (499) 135-35-34, !: +7 (499) 135-32-56
2
$ . .&. , %&',
117997, 2, . +!, 65, %
[email protected]
/!: +7 (495) 334-92-40
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɩɨɞɜɢɠɧɵɟ ɨɛɴɟɤɬɵ, ɬɟɪɦɢɧɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ, ɤɨɧɰɟɩɰɢɹ «ɜɨɡɦɭɳɟɧɧɨɝɨɧɟɜɨɡɦɭɳɟɧɧɨɝɨ» ɞɜɢɠɟɧɢɹ, ɩɪɢɧɰɢɩ ɝɢɛɤɢɯ ɬɪɚɟɤɬɨɪɢɣ, ɚɥɝɨɪɢɬɦɢɡɚɰɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ, ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ
Abstract
Recent state of terminal control theory by moving objects is described. The applied aspects of the
conception of «disturbanced – nondisturbanced» movement are analyzed. The questions of algorithmization of control problems by the movement objects on the base of the flexible traectories
principle are researched. The kinematic aspects of the realization of the given principle in the
systems of control by flight are analyzed.
ȼɜɟɞɟɧɢɟ
1 (+*) , " 1 , . ,
, , : ; ; , , ; , , - . : -
, , -
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) .
, ! , %.; " # (., , [1 3]).
* 1, (1) x = f (t , x, u ) ,
(2)
y = g(t , x ) ,
t ∈ T = [0, t F ] – ; u ∈ U = R r – " , U – ; x∈ R n - , y ∈ R m – 1, m ≤ n ; f : T × R n × U → R n g : T × R n → R m – !.
18
" Y ∗
X∗ 1:
(3) x(t F ) ∈ X∗ , y (t F ) ∈Y∗ ,
- x∗ y ∗ :
(4) x(t F ) = x ∗ , y ( t F ) = y ∗ .
+ 1 (1)-(2) " u(t ) , "
(3) (4).
Ʉɨɧɰɟɩɰɢɹ «ɧɟɜɨɡɦɭɳɟɧɧɨɝɨ-ɜɨɡɦɭɳɟɧɧɨɝɨ» ɞɜɢɠɟɧɢɹ
ɢ ɤɥɚɫɫɢɱɟɫɤɢɟ ɩɪɢɧɰɢɩɵ ɬɟɪɦɢɧɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɉɈ
" # +* - «» «» .
ɉɪɢɧɰɢɩ «ɠɟɫɬɤɢɯ» ɬɪɚɟɤɬɨɪɢɣ - «"-"» // «» (, ) 1 x∗ (t ) , " «
» . 8 u(t ) " u∗ (t ) , " "
x∗ (t ) , " " Δu(t ) :
u(t ) = u∗ (t ) + Δu(t ) ,
" " Δx(t ) - ! x(t ) x∗ (t ) , "" !:
x(t ) = x∗ (t ) + Δx(t ) .
& # « #» 1 (1)-(2), 8 # " ( ) ( ) # .
& # « »
:
(5) Δx = A (t )Δx + B(t )Δu ,
(6) Δy = C(t )Δx ,
!
A : T → R n×n , B : T → R n×r , C : T → R m×n = (1)-(2):
∗
A(t ) =
∗
∗
∂
∂
∂
f (t , x, u) , B(t ) =
f (t , x, u) , C(t ) =
g (t , x ) ,
∂x
∂u
∂x
" ( u∗ (t ) , x∗ (t ) ).
19
& «"-"»
, , #, " +* # ".
ɉɪɢɧɰɢɩ «ɝɢɛɤɢɯ» ɬɪɚɟɤɬɨɪɢɣ «», ( ) , 1, " «
» , " . 8 # « #» +* (1)-(2).
( '.'.2, «» , «» - .
ɋɨɜɪɟɦɟɧɧɵɟ ɤɨɧɰɟɩɰɢɢ ɝɢɛɤɢɯ ɬɪɚɟɤɬɨɪɢɣ
ɬɟɪɦɢɧɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɉɈ
ɉɪɢɧɰɢɩ «ɝɢɛɤɢɯ» ɬɪɚɟɤɬɨɪɢɣ +* () ! ( ) ! 1. " :
1) + ɰɢɤɥɵ, , ! ! 1 (3) (4).
() .
2) + " " , #" .
3) + " 1. «» , !
t0 x(t0 ) = x0 :
u = h(t | t0 , x0 ) ,
– ":
u(t ) = h(t | t , x(t )) .
«""» 1.. 8 (1, 2, 3) " . ( . , 1 , 3 - . " , " .
' 1. # : , " . .
+ 1 :
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* # . !!
[4]. 3 , 1 (" ), , " 1. *, " !!
(
) 1 .
! tF. *, # +* .
Ɍɟɪɦɢɧɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɉɈ ɜ ɮɢɡɢɱɟɫɤɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ
, (1), (2) (5), (6). *, " ! 1 ! . * (/&).
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; /& . (72) "
72. /& : , 8, OXYZ, 1.
, /& ! (7) r = v ,
(8) m( v + Ȧ × v ) = F ,
(9) K + Ȧ × K = M ,
K =IȦ .
r – ; v – 72; Ȧ = (ω x , ω y , ωz ) – " , ω x , ω y , ω z – ; m – , I – , K – 72; F – " # , M – " # .
6 (8) (9) # . <, " ω x , ω y , ω z < ψ, θ, γ.
(8) (9) " u = ( P, δ , δ ' , δ < ) ,
P – , δ , δ ' , δ< – , .
%# 1 1 " (7)-(9).
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%
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, > – , V – # , θ – , H – , L – # .
+ - : , ! :
(10) H = H ∗ (L) .
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ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
[1] ; &.+. (
. - 2.: % , 1984.
[2] + ;.'., +-( 4.+., & &.=., $ .+.. ;
: +
. - 2.: 2#, 1983.
[3] ; .., # 4.(., 2 &.%. $
. - 2.:
', 1989.
[4] 0 &.&., .(., " &.+., , .$. ( () // $. &' (((%. ,. . 1985. : 4. - (. 180-188.
[5] . (.&., 2# <.2., +# 4.9., ?! /.. % . $
. - 2.: 2#, 1971.
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