Robust MPC for linear systems with bounded multiplicative uncertainty

A robust tube-based Model Predictive Control (MPC) strategy is proposed for linear systems with multiplicative parametric uncertainty. The tubes are defined by sequences of polytopic sets for which we propose two methods of construction, respectively employing low-complexity parallelotopes and polytopes of fixed but arbitrary complexity. A method of computing polytopic terminal sets of arbitrary complexity is also described. An MPC law based on the minimization of an expected quadratic cost is formulated as a quadratic program. An extension to the case of probabilistic constraints requiring the online solution of a mixed-integer program is described.