Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910588856172544 |
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| author | Leeman, Antoine P. Köhler, Johannes Messerer, Florian Lahr, Amon Diehl, Moritz Zeilinger, Melanie N. |
| author_facet | Leeman, Antoine P. Köhler, Johannes Messerer, Florian Lahr, Amon Diehl, Moritz Zeilinger, Melanie N. |
| contents | System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of $\mathcal{O}(N^2 ( n_x^3 +n_u^3))$ for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to $10^3$ compared to general-purpose commercial solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions Leeman, Antoine P. Köhler, Johannes Messerer, Florian Lahr, Amon Diehl, Moritz Zeilinger, Melanie N. Optimization and Control Systems and Control System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of $\mathcal{O}(N^2 ( n_x^3 +n_u^3))$ for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to $10^3$ compared to general-purpose commercial solvers. |
| title | Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2401.13762 |