Economic model predictive control without terminal constraints: Optimal periodic operation

In this paper, we analyze economic model predictive control schemes without terminal constraints, where the optimal operating regime is not steady-state operation, but periodic behavior. We first show by means of two counterexamples, that a classical 1-step receding horizon control scheme does not necessarily result in an optimal closed-loop performance. Instead, a multi-step MPC scheme may be needed in order to establish near optimal performance of the closed-loop system. This behavior is analyzed in detail, and we derive checkable dissipativity-like conditions in order to obtain closed-loop performance guarantees.