guidance, flight mechanics and trajectory optimization

Let Y tt) denote the observations that are made on the interval
(t,, t) , that is
The expected value of the functional J can be written as
(2.5.60)
(2.5.61)
where p(;r,v,,C) is the joint density function for x and as developed
from the density functions
included since the control
for
u(t)
f , +7 and ;r, . The vari i? ble
Y
must be
will depend on, and vary with, the
observations. Now the density P(x $W) can be expressed as
plx, $Q,t! = p(x, qvpcy!
where ptX, t/v) is the probability density of F conditioned on .
Also, the expected value of some function K(x, y' can be written a
Using this result, the performance index in Eq. (2.5.61) can be written
125