Линейные задачи оптимизации. Ч.2. Оптимальное управление линейными динамическими объектами. Лутманов С.В. - 190 стр.

UptoLike

ВУЗ: 

ПГНИУ | Пермь

Составители: 

Рубрика: 

ПРИЛОЖЕНИЕ
190
Resh1 =
DSolve@8x11'@tD 2 ∗ x11@tD+ 2 ∗ x21@tD− 30 ∗ x31@tD,
x21'
@tD 10 ∗ x11@tD− x21@tD− 35 ∗ x31@tD,
x31'
@tD 2 ∗ x11@tD− x21@tD+ x31@tD,x11@0D 1,
x21
@0D 0, x31@0D == 0<, 8x11@tD,x21@tD,x31@tD<,
t
D;
Resh2
=
DSolve@8x12'@tD 2 ∗ x12@tD+ 2 ∗ x22@tD− 30 ∗ x32@tD,
x22'
@tD 10 ∗ x12@tD− x22@tD− 35 ∗ x32@tD,
x32'
@tD 2 ∗ x12@tD− x22@tD+ x32@tD,x12@0D 0,
x22
@0D 1, x32@0D == 0<, 8x12@tD,x22@tD,x32@tD<,
t
D;
Resh3
=
DSolve@8x13'@tD 2 ∗ x13@tD+ 2 ∗ x23@tD− 30 ∗ x33@tD,
x23'
@tD 10 ∗ x13@tD− x23@tD− 35 ∗ x33@tD,
x33'
@tD 2 ∗ x13@tD− x23@tD+ x33@tD,x13@0D 0,
x23
@0D 0, x33@0D 1<, 8x13@tD,x23@tD,x33@tD<,
t
D; 88x11@t, τD<, 8x21@t, τD<, 8x3 1@t, τD<< =
8Re@x11@tDD ê. Resh1, Re@x21@tDD ê. Resh1,
Re
@x31@tDD ê. Resh1<ê. 8t → t −τ<;
88x12@t, τD<, 8x22@t, τD<, 8x32@t, τD<< =
8Re@x12@tDD ê. Resh2, Re@x22@tDD ê. Resh2,
Re
@x32@tDD ê. Resh2<ê. 8t → t −τ<;
88x13@t, τD<, 8x23@t, τD<, 8x33@t, τD<< =
8Re@x13@tDD ê. Resh3, Re@x23@tDD ê. Resh3,
Re
@x33@tDD ê. Resh3<ê. 8t → t −τ<;
X
@t, τD =
i
k
x11@t, τD x12@t, τD x13@t, τD
x21@t, τD x22@t, τD x23@t, τD
x31@t, τD x32@t, τD x33@t, τD
y
{
;
Построение матрицы перехода
MK@τD = X@t, τDê.t→ 1;
8h1@τ_D,h2@τ_D,h3@τ_D< = MK@τD
8c1, c2, c3<= XT − HMK@τDê. τ→ 0L.X0
8−67.4743, −115.885, −5.34546<
Pod@τ_, l2_, l3_D=
JJ
1− Hl2 ∗ c2 + l3 ∗ c3L
c1
∗h1@τD+ l2 ∗h2@τD+ l3 ∗ h3@τDN.
J
1− Hl2 ∗ c2 + l3 ∗ c3L
c
1
∗h1@τD+ l2 ∗h2@τD+ l3∗ h3@τDNN^
1
2
                                                ПРИЛОЖЕНИЕ

Resh1 =
 DSolve @8x11 ' @t D 2 ∗ x11 @t D + 2 ∗ x21 @t D − 30 ∗ x31 @t D,
    x21 ' @t D 10 ∗ x11 @t D − x21 @t D − 35 ∗ x31 @t D,
    x31 ' @t D 2 ∗ x11 @t D − x21 @t D + x31 @t D, x11 @0 D 1,
    x21 @0 D 0, x31 @0 D == 0 <, 8x11 @t D, x21 @t D, x31 @t D<,
  t D;
Resh2 =
 DSolve @8x12 ' @t D 2 ∗ x12 @t D + 2 ∗ x22 @t D − 30 ∗ x32 @t D,
    x22 ' @t D 10 ∗ x12 @t D − x22 @t D − 35 ∗ x32 @t D,
    x32 ' @t D 2 ∗ x12 @t D − x22 @t D + x32 @t D, x12 @0 D 0,
    x22 @0 D 1, x32 @0 D == 0 <, 8x12 @t D, x22 @t D, x32 @t D<,
  t D;

 DSolve @8x13 ' @t D 2 ∗ x13 @t D + 2 ∗ x23 @t D − 30 ∗ x33 @t D,
Resh3 =

    x23 ' @t D 10 ∗ x13 @t D − x23 @t D − 35 ∗ x33 @t D,
    x33 ' @t D 2 ∗ x13 @t D − x23 @t D + x33 @t D, x13 @0 D 0,
    x23 @0 D 0, x33 @0 D 1 <, 8x13 @t D, x23 @t D, x33 @t D<,
  t D; 88x11 @t, τD<, 8x21 @t, τD<, 8x31 @t, τD<< =
 8Re@x11 @t DD ê. Resh1, Re @x21 @tDD ê. Resh1,
    Re @x31 @t DD ê. Resh1 < ê. 8t → t − τ<;
88x12 @t, τD<, 8x22 @t, τD<, 8x32 @t, τD<< =
 8Re@x12 @t DD ê. Resh2, Re @x22 @tDD ê. Resh2,
    Re @x32 @t DD ê. Resh2 < ê. 8t → t − τ<;
88x13 @t, τD<, 8x23 @t, τD<, 8x33 @t, τD<< =
 8Re@x13 @t DD ê. Resh3, Re @x23 @tDD ê. Resh3,
    Re @x33 @t DD ê. Resh3 < ê. 8t → t − τ<;
          i x11 @t, τD x12 @t, τD x13 @t, τD y
X @t, τD = x21 @t, τD x22 @t, τD x23 @t, τD ;
          k x31 @t, τD x32 @t, τD x33 @t, τD {
        Построение матрицы перехода
MK @τD = X @t, τD ê. t → 1;
8h1 @τ_D, h2 @τ_D, h3 @τ_ D< = MK @τD
8c1, c2, c3< = XT − H MK@τD ê. τ → 0L.X0

8−67.4743, − 115.885, − 5.34546<



Pod@τ_, l2_, l3_D =
    1 − Hl2 ∗ c2 + l3 ∗ c3L
 JJ                          ∗ h1@τD + l2 ∗ h2@τD + l3 ∗ h3@τDN.
       1 − Hl2 ∗ c2 + l3 ∗ c3L
               c1
    J                           ∗ h1@τD + l2 ∗ h2@τD + l3 ∗ h3@τDNN ^
                                                                      1
                  c1                                                  2



                                                       190

Страницы