Transient Performance of Tube-based Robust Economic Model Predictive Control

In this paper, we provide non-averaged and transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated both on finite and infinite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.