Robust MPC strategy with optimized polytopic dynamics for linear systems with additive and multiplicative uncertainty

Polytopic dynamics have been introduced into the predictions in Model Predictive Control (MPC) and have been optimized so as to maximize invariant ellipsoids for systems subject to multiplicative uncertainty. This work was recently extended to the case of mixed additive and multiplicative uncertainty, and sufficient conditions were provided to guarantee the invariance of an ellipsoid. Additionally, under the assumption that the multiplicative uncertainty is known during a prediction horizon NN, this extension was used as the terminal control law of an overall robust MPC strategy that deployed an affine-in-the-disturbance policy. This assumption was needed to enable the handling of constraints in the overall MPC strategy. The aims of this paper are to establish the necessity and sufficiency of the relevant invariance conditions of the polytopic dynamics, and to propose a robust MPC strategy that uses polytopic sets to describe the evolution of predicted variables and therefore does not make an assumption that future multiplicative uncertainty is known. The number of constraints and free variables of the resulting online optimization grows linearly with NN. The benefits of the strategy are illustrated by numerical simulations.