Stability in data-driven MPC: an inherent robustness perspective
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915044797710336 |
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| author | Berberich, Julian Köhler, Johannes Müller, Matthias A. Allgöwer, Frank |
| author_facet | Berberich, Julian Köhler, Johannes Müller, Matthias A. Allgöwer, Frank |
| contents | Data-driven model predictive control (DD-MPC) based on Willems' Fundamental Lemma has received much attention in recent years, allowing to control systems directly based on an implicit data-dependent system description. The literature contains many successful practical applications as well as theoretical results on closed-loop stability and robustness. In this paper, we provide a tutorial introduction to DD-MPC for unknown linear time-invariant (LTI) systems with focus on (robust) closed-loop stability. We first address the scenario of noise-free data, for which we present a DD-MPC scheme with terminal equality constraints and derive closed-loop properties. In case of noisy data, we introduce a simple yet powerful approach to analyze robust stability of DD-MPC by combining continuity of DD-MPC w.r.t. noise with inherent robustness of model-based MPC, i.e., robustness of nominal MPC w.r.t. small disturbances. Moreover, we discuss how the presented proof technique allows to show closed-loop stability of a variety of DD-MPC schemes with noisy data, as long as the corresponding model-based MPC is inherently robust. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11859 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stability in data-driven MPC: an inherent robustness perspective Berberich, Julian Köhler, Johannes Müller, Matthias A. Allgöwer, Frank Systems and Control Optimization and Control Data-driven model predictive control (DD-MPC) based on Willems' Fundamental Lemma has received much attention in recent years, allowing to control systems directly based on an implicit data-dependent system description. The literature contains many successful practical applications as well as theoretical results on closed-loop stability and robustness. In this paper, we provide a tutorial introduction to DD-MPC for unknown linear time-invariant (LTI) systems with focus on (robust) closed-loop stability. We first address the scenario of noise-free data, for which we present a DD-MPC scheme with terminal equality constraints and derive closed-loop properties. In case of noisy data, we introduce a simple yet powerful approach to analyze robust stability of DD-MPC by combining continuity of DD-MPC w.r.t. noise with inherent robustness of model-based MPC, i.e., robustness of nominal MPC w.r.t. small disturbances. Moreover, we discuss how the presented proof technique allows to show closed-loop stability of a variety of DD-MPC schemes with noisy data, as long as the corresponding model-based MPC is inherently robust. |
| title | Stability in data-driven MPC: an inherent robustness perspective |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2205.11859 |