Abstract
The discrete optimal finite preview control problem is formulated and its solution is presented. It is assumed in the present problem that the controller can make use of a preview information with respect to the command signal and/or a disturbance from the present time i up to Nla time units in the future beyond i. Nla is called the preview time and usually Nla<N, the duration of problem, over which the optimality is evaluated. The combination of the local future information from the preview and the grobal cost functional is a unique feature of the optimal finite preview control problem. The steady state solution is obtained, and it is applied to a class of vibration problems (the design of a vehicle suspension system). The evaluation of optimal cost functional values for different preview lengths and the simulation results indicate that the preview improves the performance of the system drastically.
