guidance, flight mechanics and trajectory optimization

once again due to Dynamic Programming concepts.) The number of additions
performed in the previous problem were 66 for the second table, and 11 for
the third table - for a total of 77 additions, The "brute force" method
would require the calculation of S = Xl2 t 2X22 + X32 for all possible
permutations of xl, x2, and x3 where 05 Xi5 10, + x2 t x3 = 10,
and Xi is an integer. For this particular problem the "f brute force"
method requires 66 cases or 132 additions. It is seen that even on this
simple problem the savings in additions is quite significant.
In order to compare and contrast the Dynamic Programming solution of
this problem with the classical solution, the same problem will not be
solved using classical techniques. First, the constraint equation is joined
to the original problem by a Lagrange Multiplier,
Now the partial derivatives are taken with respect to the independent
variables and equated to zero.
This yields
2s
- =2x,--h =o
a x,
h
x, = -
2
2
3 = 7
A
x3 = -
2
39
(2.2.29)
(2.2.30a)
(2.2.30b)
(2.2.30~)
(2.2.31a)
(2.2.3lb)
(2.2.31~)