Iterative computation procedures for an optimum control problem

The control problem treated here may be stated as follows: Given
\dot{x} = A(t)x+b(t)u(t)
and an initial condition
x(0)
find a control function
u(t)
such that
|u(t)|\leq 1
for
0 \leq t\leq T
and such that the inner product
[x(T), x(T)]
is a minimum. A theoretical basis for describing iterative procedures used for computing the solution to this problem is developed. A new computational procedure which does not require storing the control function from one iteration to the next is specified. The hybrid computer mechanization of this procedure is described and analog computer results illustrating the practicality of the method are presented.