Tube-based robust MPC with adjustable uncertainty sets using zonotopes

A tube-based robust Model Predictive Control (MPC) formulation with adjustable uncertainty sets is presented where the size of the uncertainty set is optimized as part of the underlying optimization problem. To guarantee constraint satisfaction subject to uncertainties bounded to this set, Robust Positively Invariant (RPI) set computation and constraint tightening are integrated into the optimization problem. Zonotopes are used to represent the set containment conditions that define RPI sets and constraint tightening as linear constraints. The Hausdorff distance metric is shown to reduce conservatism when optimizing the size of these tightened constraint sets. Finally, a numerical example demonstrates the ability to optimize the size of the uncertainty set within a robust MPC formulation and highlights the benefits and limitations of this approach.