Economic NMPC

Abstract

Economic nonlinear model predictive control is the common name for NMPC schemes in which the stage cost does not penalize the distance to a predefined equilibrium, which was one of the key assumptions in Chaps. 5 and 6. Instead, the cost can, in principle, model all kinds of quantities, like energy consumption, yield of a substance, income of a firm, etc., which one would like to minimize or maximize. In such a general setting, it is by no means clear that the moving horizon MPC paradigm yields well-performing closed-loop solutions. It was first observed by Amrit, Angeli, and Rawlings in 2012 (extending earlier work by Diehl, Amrit, and Rawlings) that strict dissipativity is a sufficient systems theoretic property for ensuring proper performance of economic MPC. In this chapter, we will rigorously establish stability as well as averaged and non-averaged performance estimates for strictly dissipative economic MPC problems, both with and without terminal conditions.