Asymmetric constraints with polyhedral sets in MPC with application to coupled tanks system

Asymmetric constraints have not received sufficient attention in the model-based predictive control (MPC) literature possibly due to the popularity of ellipsoidal terminal regions which, for asymmetric constraints, would result in conservative results. The work here adopts low complexity polyhedra for which invariance and feasibility under asymmetric constraints can be handled through the use of Farkas´ lemma and the related results. The paper embeds these results into a MPC law based on a dual mode prediction strategy and proposes algorithms for the systematic design of the polyhedral terminal sets. The efficacy of the results is illustrated through application to a coupled tanks system.