Dissipativity and Economic Model Predictive Control for Optimal Set Operation

Tim Martin, Philipp N. Köhler, Frank Allgöwer

Abstract: The paper deals with systems which are optimally operated when the system states remain in a certain subset of the state space. We define this mode of optimal operation as optimal set operation. We characterize optimal set operation by a dissipativity condition with a parametric storage function. Both, the definition and the dissipativity condition for optimal set operation, constitute a generalization of the definition and the dissipativity condition for the well-studied scenarios of optimal steady-state or optimal periodic operation. Furthermore, we present an economic MPC scheme with optimized terminal equality constraint that yields convergence of the MPC closed-loop system to the set where the system is optimally operated.