On stability and non-averaged performance of economic MPC with terminal conditions for optimal periodic operation

TL;DR

This paper proves stability and performance bounds for economic MPC schemes that operate periodically, using terminal conditions and Cesàro summation to better handle systems with optimal periodic operation.

Contribution

It extends existing methods by providing stability guarantees and non-averaged performance bounds for economic MPC in periodic operation scenarios.

Findings

Established asymptotic stability for economic MPC with terminal conditions.

Derived non-averaged performance bounds using Cesàro summation.

Provided insights into systems with optimal periodic operation.

Abstract

Operation at steady state is often not optimal when optimizing over an economic cost objective. In many cases, periodic operation yields better performance. Therefore, we derive asymptotic stability guarantees of an economic model predictive control scheme with terminal conditions for systems with optimal periodic operation for a more general setup than existing methods can handle. Moreover, we establish a non-averaged closed-loop performance bound by defining the closed-loop cost via a Ces\`aro summation instead of ordinary summation. Such a non-averaged performance bound provides new insights for systems with periodic optimal operation.