guidance, flight mechanics and trajectory optimization

3.0 RECOMMENDED PROCEDURES
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The preceding sections of this report have illustrated the dual nature
of Dynamic Progr amming as both a theoretical and computational tool. It
is the general consensus of opinion (see Ref. (2.4.1)) that on the theore-
tical level, Dynamic Progr amming is not as strong or as generally applicable
as either the Calculus of Variations or the Maximum Principle. However,
the relative strengths and weaknesses of Dynamic Programming when compared
with the variational methods are of little importance. What is important
is the fact that Dynamic Programming is a completely different approach to
optimization problems and its use can provide perspective and insight into
the solution structure of a multistage decision processes. Furthermore,
there are some problems that are rather difficult to attack using the
classical methods, but which readily yield to solution by means of Dynamic
Programming. One such example is the stochastic decision problem treated
in Section (2.5).
On the computational side, Dynamic Programming has no equal as far as
versatility and general applicability are concerned. Almost all optimization
problems can be cast in the form of a multistage decision processes and
solved by means of Dynamic Programming. However, it frequently happens
that certain problems, or certain types of problems, are more efficiently
handled by some other numerical method. Such is the case, for example,
in regard to the trajectory and control problems normally encountered in
the aerospace industry.
It has been amply demonstrated in the last few years that optimal
trajectory and control problems can be solved using a variational formulation
procedure coupled with a relatively simple iterative technique such as
quasilinearization (Ref. (3.1)), steepest ascent (Ref. 3.2)) or the
neighboring extermal method (Ref. (3.3)). The voluminous number of papers
and reports dealing with problem solution by this method attest to its
effectiveness. On the other hand, there are relatively few reports which
treat trajectory or control problems using Dynamic Programming. The reason
for this can be partially attributed to the ffnewness'f of Dynamic Programming
and the fact that other numerical procedures were available and were used
before Dynamic Programming "caught on." More important, however, is the
fact that solution generation by means of Dynamic Programming usually
requires more computation, more storage, and more computer time than do
the other numerical methods.
The role of Dynamic Programmin g in the flight trajectory and control
area should increase in the not too distant future. Presently used techniques
have been pushed almost to their theoretical limits and leave something to
be desired as more complex problems are considered and more constraint
conditions included. Dynamic Progr amming, on the other hand, is limited
only by the computer, a limitation which is continuously on the decrease
as more rapid and flexible computing equipment is developed.
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