Optimal continuous finite preview problem

This short paper deals with the preview problem, in which a controller can use future information as well as present and past information in deciding the control. The problem of following command signals is considered for the continuous time system. It is assumed that the controller can make use of the finite preview information with respect to command signal from the present time
t
up to t
la
time units in the future. t
la
is called the preview length and usually
t_{la} < T
, the duration of the problem, which distinguishes the present problem from the optimal tracking problem. It is shown how to utilize the local future information obtained by finite preview to minimize an optimality criterion evaluated over the problem duration. An example is given to show advantages of making use of future information and the existence of an effective preview length.