On the Numerical Solution of Discounted Economic NMPC on Infinite Horizons

In this work, two numerical solution methods are presented for discounted economic nonlinear model predictive control on infinite horizons without terminal constraints. While the first formulation simply replaces the infinite by a finite horizon, the second formulation uses a time transformation function to project the infinite to a finite horizon. For the first formulation, an algorithm is presented which heuristically determines a sufficiently long final time with the help of the turnpike property in order to ensure good closed-loop control performance. For the second formulation, a two-stage formulation is introduced to deal with large differences in the dynamics of the objective function and the states. The solution accuracy is improved for both formulations by using a control vector adaptation strategy such that an adequate number of decision variables is obtained. Both solution methods are compared in a case study.