guidance, flight mechanics and trajectory optimization

I. -.
In order to give an appreciation for the need for more sophisticated tech-
niques, a sample problem will be worked by the Dynamic Programming techniques
which have been discussed. The presentation will serve two purposes: first,
it will illustrate the use of Dynamic Programming on a multi-dimensional
allocation problem and, second,- it will demonstrate the rapid growth of
storage requirements as a function of the dimension of the problem. The
method of approximation in policy space will then be discussed in order to
illustrate the savings in storage requirements and the increase in computa-
tion time.
Consider the problem of minimizing the function
subject to the constraint that
and
(2.3.4)
z, + x2 + x3 = 3 (2.3.5)
VJ + fi + $5 = 3 (2.3.6)
Obviously, using Dynamic Programming to find a solution to this problem is
not very efficient. The method of Lagrange multipliers is by far a more
suitable method. However, the Dynamic Programming solution will be shobm
for illustrative purposes.
First, the problem i.s reduced to a series of simpler problem.
53
(2.3.7)
(2.3.8)
(2.3.9)