guidance, flight mechanics and trajectory optimization

and the boundary conditions
The optimal control takes the form
5(Q) =A
Be+) = 0
(2.5.106~)
u = 4, trlffirs i? (2i5.107)
The one remaining consideration is the selection of the matrix A
so that the terminal constraint of Eq. (2.5.87) is satisfied.. This
point will be treated next.
I& 2 denote the expected value of t conditioned only on the initial
information so= &, but using the optimal control of Eq. (2.5.107);
that is, 2 (t1 would be the value which would be predicted for I(t) if
the prediction were being made at time to . Similarly, let P denote
the variance of L conditioned on the same information. Thus,
and
2 = E (2)
(2.5.108)
P=E@2j (2.5.109)
Differentiating these expressions and making use of Eqs. (2.5.100) and
(2.5.107) provides
.
.L -HaGQ;'&bL 's;
(2.5.110)
p= - H&Q;'GT$#+rSf' - P.$H4W&7tTkr +#4fl&kT
while the boundary conditions are
2 (f.7) = ;,
P (*cd = io 2,'
Thus, a terminal constraint on r(Z, &"r) has been reduced to a con-
straint on P (t4) since
(2.5.111)
(2.5.112~)
(2.5.112B)
(2.5-113)
The correct value of A , that is, the value of A which will satisfy the
terminal constraint, can now be determined by the simultaneous solution
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