guidance, flight mechanics and trajectory optimization

subject to the state equations
1 = HtpGU t H$q
and a terminal constraint on the quantity Jz (q zf', - The initial
state t. is a Gaussian variable with mean and covariance given in
Eq. (2.5.96).
(2.5.115)
Let 2 denote the expected value of t and P its covariance; that is,
2 = E (Zj =H@E(X)
P
(&s - 2,
= bflp& (X-3 (X-3 4THT (2.5.116)
Now, the expected value and covariance of X were calculated for the
perfectly inobservable treatment given in Section (2.5.22) [see Eq.
(2.5.36)] . Substituting these expressions into (2.5.116) provides
with the boundary conditions
Also, letting
it follows that
3: = H&U
; =h~x~‘w
Z=
;+z
E (z) =E (2 f--j= 0
t’ = WV
Thus, substituting the value for 7 given in (2.5.119) into (2.5.114)
reduces the performance index to
141
(205.117)
(2.5.118)
(2.5.119)
(2.5.120)
(2.5.12oA)