Tube-based robust economic model predictive control

• A framework for dealing with disturbances in an economic MPC setup is introduced.
• The disturbances are considered taking RCI sets of the error dynamics into account.
• We prove robust performance estimates for the closed-loop system.
• Based on dissipativity, robust optimal steady-state operation and robust stability of the closed-loop system are shown.
• The proposed algorithm is applied to a simple CSTR model and a simple nonlinear example.

In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. Instead of simply transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework, we rather propose to consider the influence of the disturbance explicitly within the design of the MPC controller, which can lead to an improved closed-loop average performance. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that the algorithm enjoys similar properties as a nominal economic MPC algorithm (i.e., without disturbances), in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system, as well as stability and optimal steady-state operation.