Recursively feasible Robust MPC for linear systems with additive and multiplicative uncertainty using optimized polytopic dynamics

A recent paper, which considered multiplicative uncertainty, introduced polytopic dynamics into the prediction structure and optimized these so as to maximize the volume of an invariant ellipsoid. This work was extended to the case of mixed additive and multiplicative uncertainty with conditions that are claimed only to be sufficient. Additionally, when the system dynamics are known over a prediction horizon, N, the derived control law was used as the terminal control law of an overall robust MPC strategy that deployed an affine-in-the-disturbances policy. The aim of this paper is to reformulate the conditions of the polytopic dynamics such that the invariance conditions are both necessary and sufficient, and to deploy an overall robust MPC scheme using the polytopic dynamics without the requirement that the system dynamics are known over the prediction horizon. The results of the paper are illustrated by means of a numerical example.