:
;
, , , ;
, ;
, , .
S N . i - x(i) = (x1(i), x2(i),,xni(i)) , . s(i) = s(x(i)), . , - .
x s(x), .
, .
, , .
s(i)max, s(i)min, s(i)opt
- , i - , (smax, smin, sopt).
(), 0, 1 - , :
Δ = 0 - 1.
Δ ( ), - . Δ - , ( Δ > 0 - , Δ < 0 - ).
. .
, - smin smax.
F(s(t), u(t)),
s(t) - t, u(t) - , , uopt - U, t0 < t < T, smin s smax.
:
H = |(Fmax - Fmin) / (Fmax + Fmin)|,
Fmax = max F(uopt, smax), Fmin = min F(uopt, smin),
t [t0;T ], s [smin; smax].
.
, , :
1. (), :
( 0 < T < ∞, t: (i)(s; s(i), t) = (i)(s; s(i), t + T),
|
|
(i)(s; s(i), t) = (i)(s; s(i), t + T)).
2. , :
(s(x) 0 i = 1, 2,..., n) => ( (i) 0, (i) 0).
3. : (i), (i) , , s(i)opt, sopt x(i)opt, xopt . , , , ( ).
(ij)(s; s(i), s(j), t) i j . (i), (i) - :
i, , . , .
(t; t + τ)
, τ > 0
() .
- ,
(τ, t, x) (0 < t <T, 0 < x < 1, 0 < τ < T)
. , , ( ).
:
(τ, t, x) = 0 + 1x,
- . , a - , b - :
(τ) = 0(τ) + 1(τ) x(τ) > 0.
x = 0. :
- λ, - λ.
. , , 1.
, ds/dt - , ds1/dt - , , ds2/dt - (, , , ), . :
ds/dt = ds1/dt + ds2/dt.
- , , , (, .), (, ).
. Ω, ( ) xi, i = 1, 2, , n. xi [ti-1; ti]. (, , ). () rij,
R = {rij: i = 1, 2,, n-1; j = 2, 3,, n}.
|
|
: - , . , :
F - S.
xi, - . xi, .
rij , , , :
vij - , xi xj ( ), hj - , xj τi, () . .
, , .
.
"" , , .
- , .
(), .
, . - .
. (): f(i), i - n , , n = 5, i = (1, 0, 0, 1, 0). , "" . :
1. ( ) - I0 = (i1, i2,:, in), ij {0,1} "" , , , , ;
2. k = 0, f0 = max{f(i), i I0};
3. ():
() () i1, i2 ( );
( ) i;
( );
f0 < f(i) f0 = f(i);
( );
k = k + 1
( , ).
f(i).
() i1, i2 i, 0.5 - . . , .
. , (0 1, ).
.
, , , , , . " ".
|
|
, , , .
, , , , , , .