An efficient algorithm for discrete-time H_∞ preview control

An efficient numerical solution to the output feedback, discrete-time, H_∞ preview control problem is presented. The first step of the solution comes from embedding the preview control problem in a two-degree-of-freedom generalised regulator framework, in which the augmented system state includes a segment of the (frequency weighted) previewed signal. An efficient method for solving the resulting inflated Discrete Algebraic Riccati Equations (DAREs) is then found. It is demonstrated that one need only solve an (estimation) Riccati equation with dimension that of the plant, and a control Riccati equation with dimension that of the plant and reference weighting taken together. The reduced control Riccati equation is the product of a recursive reduction, enabled by the zero eigenvalues in the associated closed-loop matrix. An added feature of the presented algorithm is that no 'large' matrix computations are required and no large matrices need be stored; only the edges of the full information Riccati equation solution are required when synthesising the controller.