Min–Max MPC based on a network problem

In general, min–max model predictive controllers have a high computational burden. In this work, an efficient implementation of this class of controllers that can be applied to linear plants with additive uncertainties and quadratic cost functions is presented. The new approach relies on the equivalence of the maximization problem with a network problem. If a given condition is satisfied, the computational burden of the proposed implementation grows polynomially with the prediction horizon. In particular, the resulting optimization problem can be posed as a quadratic programming problem with a number of constraints and variables that grows in a quadratic manner with the prediction horizon. An alternative controller has been proposed for those systems that do not satisfy this condition. This alternative controller approximates the original one with a given bound on the error.