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 (DM) mechanism to translate a high-level preference into a single solution. To this aim, we introduce an approach called individual minima-informed DM. 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 (PFs) and leverage the individual minima (IM), which are characteristic Pareto-optimal points. By this, we aim to facilitate mapping a high-level preference to a point on the PF. Several approaches exist to guarantee the closed-loop stability of an MOMPC scheme. This work builds upon an approach known from the literature, which combines a quasi-infinite horizon scheme with an additional descent condition on the costs. Assuming that the terminal ingredients of the quasi-infinite horizon approach are fixed, then the size of a PF or the DM space is determined solely by the descent condition. This paper examines both the IM-informed DM methods and their integration into a stabilizing MOMPC scheme. The main contributions are twofold. First, we propose and systematically analyze six variants of IM-informed DM methods, including two novel methods, designed to facilitate the translation of a high-level preference to a point on the PF. Second, to retain the largest possible DM space for these methods, we show that they can be embedded into an MOMPC framework while preserving closed-loop stability under a descent condition that is less restrictive than in the literature. We further present a practical method for constructing the required terminal ingredients. A numerical case study confirms the closed-loop stability of the proposed framework and illustrates the potential benefit of adapting the preference online.