Robust and stochastic linear MPC for systems subject to multiplicative uncertainty

A robust Model Predictive Control (MPC) strategy is proposed for linear systems with multiplicative uncertainty. The uncertainty in the prediction horizon is bounded by sequences of polytopic sets of fixed but arbitrary complexity. A method of computing polytopic terminal sets of arbitrary complexity is also described. An MPC law based on the minimisation of an expected quadratic cost is formulated as a quadratic program. An extension to the case of probabilistic constraints requiring the solution of a mixed-integer program is described, which exhibits low conservatism with respect to constraint violations.