guidance, flight mechanics and trajectory optimization

The integral in Equation 2.2.1 can now be written in its discrete form as
i=l
(2.2.2)
The evaluation of the ith term can be seen for a typical transition in the
above sketch. The choiz of yt. can be thought of as being the decision
parameter. The similarities to'the previous examples should now be evident.
Each transition in the space has an associated "cost" just as in the previous
travel problem. The problem is to find the optimum path from (x0, y ) to
(XfJ Yf)
such that J, or the total cost, is minimized. Obviously, i? a
fairly accurate solution is desired, it is not advantageous to choose big
increments when dividing t@e space. It must be kept in mind, however, that
the amount of computationinvolved increase quite rapidly as the number of
increments increases. A trade-off must be determined by the user in order
to reach a balance between accuracy and computation time.
The problem of Mayer can be shown to be equivalent to the problem of
Lagrange (see Ref. 2.1). This problem will be included in this discussion
because it is the form in which guidance, control and trajectory optimization
problems usually appear. The general form of the equations for a problem of
the Mayer type can be written as
2 =f (%, u) (2.2.3)
15