Stability of multiobjective predictive control: A utopia-tracking approach

We propose a utopia-tracking strategy to handle multiple conflicting objectives in model predictive control. The controller minimizes the distance of its vector of objectives to that of the compromise solution: the point along the steady-state Pareto front closest to the utopia point, where all the objectives are independently minimized. We establish conditions for asymptotic stability and propose numerical implementation variants. One of the key advantages of the approach is that it avoids the computation of Pareto fronts in real-time environments. In addition, the approach can handle general objectives of different nature such as economic and regularization.