Economic model predictive control without terminal constraints for optimal periodic behavior

In this paper, we analyze economic model predictive control schemes without terminal constraints, where the optimal operating behavior is not steady-state operation, but periodic behavior. We first show by means of a counterexample, that a classical receding horizon control scheme does not necessarily result in an optimal closed-loop behavior. 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 show that under suitable dissipativity and controllability conditions, desired closed-loop performance guarantees as well as convergence to the optimal periodic orbit can be established.