Average Constraints in Robust Economic Model Predictive Control∗

In this paper, we extend a previously introduced methodology for tube-based robust economic MPC to consider nonlinear average constraints, i.e., constraints on system states and inputs that need to be satisfied on average. A specifically defined integral stage cost takes the disturbance into account when considering the performance. The key idea is to use an appropriately tightened version of the average constraints by using a modified auxiliary output function in their formulation. By means of the tightened constraints, satisfaction of the original average constraints can be guaranteed despite disturbances acting on the system. For some special cases, we provide concepts to simplify the tightening (which might in general be difficult to determine). In addition, we discuss how average constraints can be used in order to enforce convergence of the closed-loop system to an invariant set. Finally, the proposed approach is illustrated with a numerical example.