On convergence and performance certification of a continuous-time economic model predictive control scheme with time-varying performance index

This paper addresses the design of convergence and performance certified sampled-data model predictive control (MPC) laws with a time-dependent economic performance index. More precisely, using a dissipativity property of the system, we provide a set of sufficient conditions that guarantee convergence of the closed-loop state trajectory to a, possibly time-varying, average economically optimal state trajectory. Moreover, the average performance of the closed-loop system is shown to be no worse than the one obtained by operating the system at the average economically optimal state trajectory. Constructive methods to design an appropriate terminal set and terminal cost that satisfy the proposed sufficient conditions are presented and illustrated with numerical examples.