guidance, flight mechanics and trajectory optimization

Since the quantity Q(-k+) is independen$ of the control action
(see (2.5.117)), a*cons%raint on -e(+Z,) is equivalent to a constraint
on the quantity ff ;,' .' Let
then from (2.5.117) and (2.5.125)
with
w(t)= a7
(2.5.126)
% = 2, ;: (2.5.127)
Thus A is to be selected so that the simultaneous solution of the 5 and w
equations, which satisfies the boundary conditions of Eq. (2.5.124) and
(2.5.LZ'7), provides a value of WJ(t,) which satisfies the terminal
constraint. As in the previous case, the solution will usually require
iteration. However, the matrix A is again negative semi-definite and
this condition will aid in the iteration process.
2.5.3.3 Partially Qbservable Case
The problem is to select the control a to minimize the functional
subject to the state equation
E (J) = E {l:fTQ t + UrQ, U) dt + S&L 2+ (2.5.128)
0
2 = H#GU + n4f
and a termi,nal constraint on E (z+ $1 In this case, however, observations
of the state variable x are made continuously as represented by the
observation equation
Y' hdx+JL
(2.5.129)
where q is a Gaussian white noise with zero mean and variance r(t) ;
that is,
& (qj = O
143
(2.5.130)