Линейные задачи оптимизации. Ч.2. Оптимальное управление линейными динамическими объектами. Лутманов С.В. - 187 стр.

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ПРИЛОЖЕНИЕ
187
Resh1 =
NDSolveA9x11'@tD x31@tD,x21'@tD == x41@tD,
x31'
@tD Cos@tD∗ x31@tD+ t ∗ x41@tD,
x41'
@tD
1
t + 1
∗ x31@tD+ Sin@tD∗ x41 @tD,x11@0D 1,
x21
@0D 0, x31@0D == 0, x41@0D == 0=,
8x11@tD,x21@tD,x31@tD,x41@tD<, 8t, 0, 1<E;
Resh2
=
NDSolveA9x12'@tD x32 @tD,x22'@tD == x42@tD,
x32'
@tD Cos@tD∗ x32@tD+ t ∗ x42@tD,
x42'
@tD
1
t + 1
∗ x32@tD+ Sin@tD∗ x42 @tD,x12@0D 0,
x22
@0D 1, x32@0D == 0, x42@0D == 0=,
8x12@tD,x22@tD,x32@tD,x42@tD<, 8t, 0, 1<E;
Resh3
=
NDSolveA9x13'@tD x33 @tD,x23'@tD == x43@tD,
x33'
@tD Cos@tD∗ x33@tD+ t ∗ x43@tD,
x43'
@tD
1
t + 1
∗ x33@tD+ Sin@tD∗ x43 @tD,x13@0D 0,
x23
@0D 0, x33@0D 1, x43@0D == 0=,
8x13@tD,x23@tD,x33@tD,x43@tD<, 8t, 0, 1<E;
Resh4
=
NDSolveA9x14'@tD x34 @tD,x24'@tD == x44@tD,
x34'
@tD Cos@tD∗ x34@tD+ t ∗ x44@tD,
x44'
@tD
1
t + 1
∗ x34@tD+ Sin@tD∗ x44 @tD,x14@0D 0,
x24
@0D 0, x34@0D 0, x44@0D 1=,
8x14@tD,x24@tD,x34@tD,x44@tD<, 8t, 0, 1<E;
88x11@tD<, 8x21@tD<, 8x31@tD<, 8x41@tD<< =
8x11@tDê. Resh1, x21@tDê. Resh1, x31@tDê. Resh1,
x41
@tDê. Resh1<;
88x12@tD<, 8x22@tD<, 8x32@tD<, 8x42@tD<< =
8x12@tDê. Resh2, x22@tDê. Resh2, x32@tDê. Resh2,
x42
@tDê. Resh2<;
88x13@tD<, 8x23@tD<, 8x33@tD<, 8x43@tD<< =
8x13@tDê. Resh3, x23@tDê. Resh3, x33@tDê. Resh3,
x43
@tDê. Resh3<;
88x14@tD<, 8x24@tD<, 8x34@tD<, 8x44@tD<< =
8x14@tDê. Resh4, x24@tDê. Resh4, x34@tDê. Resh4,
x44
@tDê. Resh4<;
                                     ПРИЛОЖЕНИЕ

Resh1 =
 NDSolve A9x11 ' @t D      x31 @t D, x21 ' @t D == x41 @t D,
   x31 ' @t D Cos @t D ∗ x31 @t D + t ∗ x41 @t D,
   x41 ' @t D        ∗ x31 @t D + Sin @t D ∗ x41 @t D, x11 @0 D
                1
                                                                     1,

   x21 @0 D 0, x31 @0 D == 0, x41 @0 D == 0 =,
              t+1

  8x11 @tD, x21 @t D, x31 @tD, x41 @tD<, 8t, 0, 1

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