guidance, flight mechanics and trajectory optimization

are applied to Min (fl), the range of Min (f ) can be found for various
admissible values of xl. This step can be thought of as the first stage
of a three stage decision process, where the various choices for xl can
be as many as desired within the limits 0=X, 4/O.
Now that all the choices for the first decision have been investigated,
the second decision must be considered. Again, care must be taken in the
specification of the constraint equations. The optimal value function for
the second decision is
The constraints on 3 and x2 are chosen to be
$=(-+2X; (2.2.26)
X, + x2 = AZ OLAz g 10 (2.2.27)
For each value of A2 that is to be investigated, there are many combinations
of x, and x2 to be considered. More precisely, the number of combinations
of "I and x2 to be considered is the same as the number of AlIs that are
less than or equal to the A being considered, e.g., if Al was investigated
for comb~a;i~~s5~u,'I A ;de&=tiedis 5 being considered, then the following
A
- %, - x2
0 5
5- 0
The third decision does not require as much computation as the others in this
case because of the original constraint equations.
;“, + xz f z 3
XL ZO
Since the first
%and +x
"1 2'
two decisions were investigated for many possible
it is only necessary to consider
values of
= /o
x, f x2 + x3 = IO
because the various choices for will specify 5 + x2 = 10 - 3 and these
possibilities have already been 3 ' vestigated.
(2.2.28)
The arithmetic solution will now be shown so that the previous discussion
will be clear. For simplicity, only integers will be considered for the
allowable values for xl, x2, and x3. A table can be constructed for the
first decision as follows:
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