Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908304910843904 |
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| author | Xie, Yifan Berberich, Julian Strässer, Robin Allgöwer, Frank |
| author_facet | Xie, Yifan Berberich, Julian Strässer, Robin Allgöwer, Frank |
| contents | We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization Xie, Yifan Berberich, Julian Strässer, Robin Allgöwer, Frank Systems and Control We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example. |
| title | Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.04870 |