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In this work, we study economic model predictive control (MPC) in situationswhere the optimal operating behavior is periodic. In such a setting, theperformance of a standard economic MPC scheme without terminal conditions cangenerally be far from optimal even with arbitrarily long prediction horizons.Whereas there are modified economic MPC schemes that guarantee optimalperformance, all of them are based on prior knowledge of the optimal periodlength or of the optimal periodic orbit itself. In contrast to theseapproaches, we propose to achieve optimality by multiplying the stage cost by alinear discount factor. This modification is not only easy to implement butalso independent of any system- or cost-specific properties, making the schemerobust against online changes therein. Under standard dissipativity andcontrollability assumptions, we can prove that the resulting linearlydiscounted economic MPC without terminal conditions achieves optimal asymptoticaverage performance up to an error that vanishes with growing predictionhorizons. Moreover, we can guarantee practical asymptotic stability of theoptimal periodic orbit under the additional technical assumption thatdissipativity holds with a continuous storage function. We complement thesequalitative guarantees with a quantitative analysis of the transient andasymptotic average performance of the linearly discounted MPC scheme in anumerical simulation study.

Linearly discounted economic MPC without terminal conditions for periodic optimal operation