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

Abstract: Multi-objective model predictive control (MOMPC) for fixed point stabilization requires an automated a priori decision-making mechanism to translate a high-level preference into a single solution to be implemented. To this aim, we introduce an approach called individual minima-informed decision-making. This class of methods can be implemented through two sequential optimizations, regardless of the number of objectives, thereby improving the real-time capability of MOMPC. These methods operate on Pareto fronts and leverage the individual minima (IM), which are characteristic Pareto-optimal points. By this, we aim to produce a robust translation of a high-level preference to a suitable point on the Pareto front. However, guaranteeing the closed-loop stability of the resulting MOMPC scheme remains an open challenge. This paper addresses this gap by developing a novel MOMPC framework that integrates IM-informed decision-making while formally guaranteeing asymptotic stability. Our contribution is twofold. First, we propose and systematically analyze six variants of IM-informed decision-making methods -- including two novel methods -- designed to achieve the above-mentioned translation. Second, we embed these methods into a quasi-infinite horizon MOMPC framework and provide a rigorous proof of closed-loop asymptotic stability. The proof holds for any of the presented decision-making methods and relies on a descent condition that is less restrictive than those in prior literature. The practical applicability and effectiveness of the proposed framework are demonstrated in a numerical case study.