An off line algorithm for reducing the computational burden of a MPC min max controller

We consider min max MPC for linear plants with additive bounded uncertainties and quadratic cost function. Under these assumptions, we show that it is possible to evaluate the worst case cost taking into account only a reduced set of extreme realizations of the uncertainty. The obtained set has cardinality generally several orders of magnitude smaller that the total set of extreme realizations. We provide an algorithm that computes, off-line, this reduced set for a given plant.