Robust Model Predictive Control Exploiting Monotonicity Properties

Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between conservatism and computational complexity. Monotone systems facilitate the efficient computation of reachable sets and thus the straightforward formulation of a robust model predictive control approach optimizing over open-loop predictions. We present an approach based on the division of reachable sets to incorporate feedback in the predictions, resulting in less conservative strategies. The concept of mixed-monotonicity enables an extension of our methodology to non-monotone systems. Lastly, we discuss the relation between widely used tube-based MPC approaches and our proposed methods. The potential of the proposed approaches is demonstrated through a nonlinear high-dimensional chemical tank reactor cascade case study.