Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908979181912064 |
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| author | Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin |
| author_facet | Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin Optimization and Control 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. |
| title | Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.23454 |