Abstract
The optimal finite preview control problem is formulated for the continuous time system. It is assumed in the present problem that in deciding control the controller can make use of preview information with respect to a command signal and/or a disturbance from the present time t up to tla time units in the future beyond time t. The time interval tla is called the preview time and usually tla<tf-t0, where t0 and tf are the initial time and the final time respectively. Using the local future information obtained by a finite preview, the optimal control is determined so that it minimizes the cost functional evaluated over the entire time interval [t0, tf]. The solution is obtained by dynamic programming. The steady state solution is obtained for the case when the duration of problem is infinite and the quantities that appear in the problem are all time invariant. For the trajectory following type problem, the transfer function between the command signal and the output of the optimally controlled plant is derived. An example shows the structural properties of the optimal finite preview control system.
