Economic Model Predictive Control for Robust Periodic Operation with Guaranteed Closed-Loop Performance

We present an economic model predictive control scheme for general nonlinear systems based on a terminal cost and a terminal constraint set. We study in particular systems which are optimally operated at some periodic orbit. Besides recursive feasibility of the control scheme, we provide an asymptotic average performance bound which is no worse than the performance value of the system's optimal periodic orbit. By means of a certain (strict) dissipativity assumption, asymptotic convergence to the optimal periodic orbit is shown. Using a tube-based approach, we extend our method to become applicable in the presence of unknown but bounded disturbances. In addition, we propose the concept of robust optimal periodic operation and show how it can essentially improve the closed-loop performance using a simple supply chain network example.