Reduced order of the Riccati equation and optimal preview control of singular systems

A preview control problem of a generalized discrete-time linear system was studied. First an extending error system was constructed by applying the difference method to the system equation, the error vector and the objective value signal. This converts the problem from a preview control problem of an extending system to a common control problem in analysis. Then, using the result of the optimal control theory of the generalized system, a controller with preview action of the generalized system was got. Also, a matrix Riccati equation was converted by decreasing its rank, which enables the closed-circular system.