Off-line Robustification of Model Predictive Control for Uncertain Multivariable Systems

This paper proposes an off-line state-space control methodology for enhancing the robustness of multivariable Model Predictive Control (MPC) through the convex optimization of the Youla parameter. The Youla parameter-based optimization strategy allows convex specifications in closed-loop representation, focusing on the robustification of an initial controller using LMIs (Linear Matrix Inequalities) techniques. It is well established that such kind of robustification improves among others robustness towards unstructured uncertainties, however modifying the robustness of the initial controller towards system polytopic uncertainties. On the other hand, these polytopic uncertainties are not straightforward to deal with, imposing non-convex specifications in the Youla parameter. To overcome these difficulties, a novel structure is presented, including an additional convex condition on the Youla parameter to preserve robustness of the initial controller towards system polytopic uncertainties while managing the compromise with robust stability under unstructured uncertainties for the nominal controlled system. The potential of the developed robustified multivariable MPC controller is further illustrated in simulation on a stirred tank reactor.