Geoscience Reference
In-Depth Information
According to this,
the ship will have position
ʷ
with average E
g
¼
g
1
þ
2
.
The case of arbitrary of management actions demands the fragmentation of con-
trolling
E½ T
t
1
ð
ÞDg
¼
g
1
g
1
T
t
1
ð
Þ=
ð
T
t
1
Þ
0 and dispersion D
g
¼
ð
T
t
1
Þr
values
of
|a|
by
partial
intervals
[h
i
,
h
i+1
].
Then
u
p
r
p
t
i
=
½
T
t
1
t
i
h
i
h
i
1
i ¼ 1
ð
; ...;
n
Þ;
h
0
¼ 0
;
h
n
¼ h
:
As a result,
we have:
!
T
X
n
2
2
t
n
þ
1
¼
r
2
D
g
¼
r
n
¼
r
t
j
j¼1
To determine the optimal management moments {t
i
} as functions of T,itis
necessary to form relevant equations. It is evident that value t
j
does not depend on
the number of subsequent control, but is fully de
ned by the interval [0, h] seg-
mentation. So, supposing that moments {ti}
i
} are de
ned and
xed, we have
q
T
þ
0
5y
1
y
1
25y
1
t
1
¼ T
þ
0
:
:
;
q
r
i
þ
T
T
i
t
i
þ
1
¼ T
T
i
þ
r
i
r
i
2
;
where
r
i
¼ y
i
=
2 h
i
þ
1
=
h
i
1
ð Þ;
t
n
þ
1
¼ T
T
n
;
T
i
¼ t
1
þþ
t
i
:
Above considered the case of the random deviations of the ship course as
considered above, supports the choice of the parameter a which provides the ship
arrival to an in advance de
ð
Þ
;
y
i
¼ u
p
r=
h
i
i ¼ 1
; ...;
n
1
½
ned position after each control. But another case is
possible when a is de
ned on every management stage. In this case, the ship
arrivals to the following management moment with null ordinate. If i.e. h
i
=h, the
ship hunting is not controlled, and
u
p
r
t
p
ht
i
þ
1
i ¼ 1
ð
; ...;
n
1
Þ
From this follows
s
t
l
n
þ
1
;
s ¼ 2
ð
2
j
l ¼ 2
j
t
n
j
¼
l
1
Þ;
;
l
¼ 1
=
y
;
T ¼ t
n
þ
1
þ
y
2
X
n
j¼1
l
l
2
t
n
þ
1
These equations fully and de
nitely determine the decomposition of interval
(0, T).
Finally, there is a third controlling procedure when the ship management is
realized only if it goes out of some
-stripe. In this case, the ship starting at moment
t = 0 from point O with parameters 0
ʵ
ð
; r
2
Þ
reaches some position (T,
ʷ
) with E
ʷ
=0
2
at the moment T. The management of the ship course by changing
and D
g
¼ T
r
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