Set-Theoretic Direct Data-driven Predictive Control
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912100410982400 |
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| author | Bajelani, Mohammad Lucia, Walter van Heusden, Klaske |
| author_facet | Bajelani, Mohammad Lucia, Walter van Heusden, Klaske |
| contents | Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems with unknown time delays, we propose a set-theoretic direct data-driven predictive controller that does not require a terminal cost to provide closed-loop guarantees. In particular, first, starting from input/output data series, we propose a sample-based method to build N-step input output backward reachable sets. Then, we leverage the constructed family of backward reachable sets to derive a data-driven control law. The proposed method guarantees finite-time convergence and recursive feasibility, independent of objective function tuning. It requires neither explicit state estimation nor an explicit prediction model, relying solely on input-output measurements; therefore, unmodeled dynamics can be avoided. Finally, a numerical example highlights the effectiveness of the proposed method in stabilizing the system, whereas direct data-driven predictive control without terminal ingredients fails under the same conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_00703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Set-Theoretic Direct Data-driven Predictive Control Bajelani, Mohammad Lucia, Walter van Heusden, Klaske Systems and Control Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems with unknown time delays, we propose a set-theoretic direct data-driven predictive controller that does not require a terminal cost to provide closed-loop guarantees. In particular, first, starting from input/output data series, we propose a sample-based method to build N-step input output backward reachable sets. Then, we leverage the constructed family of backward reachable sets to derive a data-driven control law. The proposed method guarantees finite-time convergence and recursive feasibility, independent of objective function tuning. It requires neither explicit state estimation nor an explicit prediction model, relying solely on input-output measurements; therefore, unmodeled dynamics can be avoided. Finally, a numerical example highlights the effectiveness of the proposed method in stabilizing the system, whereas direct data-driven predictive control without terminal ingredients fails under the same conditions. |
| title | Set-Theoretic Direct Data-driven Predictive Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.00703 |