Robust Economic Model Predictive Control without Terminal Conditions

Abstract

In this paper, a tube-based economic Model Predictive Control (MPC) scheme for systems subject to bounded disturbances is investigated that uses neither terminal costs nor terminal constraints. We provide robust guarantees on the closed-loop performance under suitable dissipativity and controllability conditions. Furthermore, we prove practical convergence to an optimal robust control invariant set, as well as its practical stability under slightly stronger assumptions. Hence, this work extends the results from nominal economic MPC without terminal conditions to systems with bounded disturbances by using similar turnpike arguments and a properly modified stage cost. The results are discussed in a numerical example.