Regret-based Robust Economic Model Predictive Control for Nonlinear Dissipative Systems

In this note, we introduce a regret-based economic MPC paradigm for nonlinear systems subject to unknown but bounded disturbances. The closed-loop system is optimized with respect to a robust regret function within a tube around the solution of the associated nominal system. The main motivation of the proposed work is the possible improvement of the economic performance when one considers the regret function as the objective function for the robust economic MPC algorithm instead of the worst cost. When the dissipativity of the nominal system with an appropriate supply rate is satisfied, the closed-loop system is proved to be driven to an optimal robust set-point under the proposed Economic MPC. Furthermore, under mild assumptions, we show that the closed-loop asymptotic average regret of the proposed controller is better than or equal to the regret at the robust steady-state. Finally, an illustrative example is utilized to compare the closed-loop stability and the average closed-loop performance (i.e., closed-loop regret and closed-loop economic cost) of the proposed regret based robust EMPC and the worst cost based EMPC.