Thomas Schmitt, Tobias Rodemann, Jürgen Adamy, "Automatized Decision Making in Multi-Objective MPC with Preferences", GMA Fachausschuss 1.40 „Systemtheorie und Regelungstechnik", 2021.

If multiple objectives have to be considered in Model Predictive Control (MPC), usually this is achieved by using a weighted sum as the cost function of the optimal control problem. where the weights are fixed. However, if the circumstances vary over time, the selected weighting between the objectives might not be desirable anymore. Thus, concepts from Multi-Objective Optimization (MOO) can be used. In MOO, the main goal is to choose the Pareto solution which represents our interest most. A solution is Pareto optimal, if there is no other solution which dominates it, i. e. which is just as good in all objectives while being even better in at least one. The set of all Pareto optimal solutions is called Pareto front. In combination with MPC, the problem can be transformed handled as a MOO problem, which means that we determine an approximation of the Pareto front at every time step. Usually, a decision maker is responsible for choosing a solution from the Pareto front. However, even with low sampling times, this would be a too tedious task. Thus, we propose an approach to automatize the decision process while respecting preferences for each objective, e. g. 50-20-30 for a 3D problem.