Geometrical characterization of robust predictive control strategies

Abstract

This paper reviews three methodologies: Model Predictive Control (MPC), Robust
MPC based on LMIs and Desensitized MPC. These are applied for uncertainty LTI models
and the necessary tools are provided for their maximal robust invariant set comparison. In the
case of a classic MPC design one can consider an explicit controller for the nominal dynamic
model (the close loop system becoming PWA polytopic) and compute its robust invariant set.
If this set is not finetly determined, a contractive algorithm can be used to obtain an outer
approximation. A certain degree of robustness can be added to such a construction by adjusting
the cost function. Such a robustified control law can be compared in terms of maximal invariant
set with the MPC schemes based on LMIs on one hand and with the desensitized version of
MPC on the other hand.