Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization

Abstract

In multi-objective model predictive control (MOMPC), a single Pareto-optimal solution has to be selected at each sampling instant by an automated a priori decision-making (DM) mechanism, since real-time constraints do not permit a human decision-maker to be involved. This paper considers MOMPC for fixed point stabilization, where the DM translates a high-level preference into the solution to be implemented, while closed-loop stability has to be preserved. To this end, an approach called individual minima-informed DM is introduced. These methods leverage the individual minima, which are characteristic Pareto-optimal points, to facilitate the translation of a high-level preference to a point on the Pareto front. They can be implemented through two sequential optimizations, regardless of the number of objectives, thereby facilitating a real-time implementation of MOMPC. Two novel methods are proposed and compared with four established ones. These methods are embedded into a stabilizing MOMPC scheme that builds on a quasi-infinite horizon framework from the literature. Closed-loop stability is proven under a descent condition that is less restrictive than the one in the original framework and retains the largest DM space among all descent conditions that prevent any objective from increasing. The required terminal ingredients can be constructed with a practical procedure. In a numerical case study, the resulting scheme stabilizes the fixed point and illustrates the potential benefit of adapting the preference online.