guidance, flight mechanics and trajectory optimization

Note that each diagonal corresponds to a particular value for x1+x2 = Al.
The optimum value for f2 in each diagonal is encircled. This chart will
be useful as soon as the graph for the third decision is found. It is shown
below:
0
1
2
3
4
5
6
7
8
9
10
G
0 1 2 3 4 5 6 7 8 9 10
Since it was specified that xl + x2 t x3 = 10, only one diagonal is
needed. The procedure to find the optimum values is now straightforward.
From the previous table it is seen that optimum decision for x3i.s x3 = 4, which
means x1 + x2 = 6. This corresponds to a value of 40 for f3. The optimum
values for xl‘ and x2 can now be determined by referring to the table for
the second decision. Since xl t x2 = 6, the best value in the sixth diag-
onal must be selected. It is 24, which corresponds to xl = 4 and x2 = 2.
Thus, the optimum values for xl, x2, and x3 have been determined to be
x1 = 4, x2 = -2, x3 = 4.
The question arises: is any savings realized by using Dynamic
Programming for this problem? In order to answer this question, the number
of computations using Dynamic Programming will be compared to that using
the "brute force" method. (It should be noted, however, that small problems
do not demonstrate the beauty of Dynamic Programming as well as larger
problems. It will be shown in Section 2.3.3.l.that some problems that are
virtually impossible to solve by the "brute force" method become reasonable
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