Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation
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| Format: | Preprint |
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2024
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| _version_ | 1866912209601298432 |
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| author | Xie, Yifan Berberich, Julian Allgöwer, Frank |
| author_facet | Xie, Yifan Berberich, Julian Allgöwer, Frank |
| contents | Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation Xie, Yifan Berberich, Julian Allgöwer, Frank Systems and Control Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods. |
| title | Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.19096 |