Offline tube design for efficient implementation of parameterized tube model predictive control

Recently introduced parameterized tube model predictive control (PTMPC) supersedes the robust model predictive control (RMPC) using the affine in the past disturbances control policy, and is, in certain cases, equivalent to RMPC utilizing dynamic programming. PTMPC online implementation reduces to a standard convex optimization for which the numbers of the decision variables and equality and inequality constraints grow quadratically with respect to the prediction horizon N. This paper considers the reduction of computational complexity to linear growth by allowing a part of the computation to be performed offline. The suggested offline simplifications preserve, to a high degree, the desirable system theoretic properties associated with PTMPC.