Stochastic Model Predictive Control for Sub-Gaussian Noise
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915558999457792 |
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| author | Ao, Yunke Köhler, Johannes Prajapat, Manish As, Yarden Zeilinger, Melanie Fürnstahl, Philipp Krause, Andreas |
| author_facet | Ao, Yunke Köhler, Johannes Prajapat, Manish As, Yarden Zeilinger, Melanie Fürnstahl, Philipp Krause, Andreas |
| contents | We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can provide guarantees for a large class of distributions, including time-varying distributions. Specifically, we first provide a new characterization of sub-Gaussian random vectors using matrix variance proxy, which can more accurately represent the predicted state distribution. We then derive tail bounds under linear propagation for the new characterization, enabling tractable computation of probabilistic reachable sets of linear systems. Lastly, we utilize these probabilistic reachable sets to formulate a stochastic MPC scheme that provides closed-loop guarantees for general sub-Gaussian noise. We further demonstrate our approach in simulations, including a challenging task of surgical planning from image observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Model Predictive Control for Sub-Gaussian Noise Ao, Yunke Köhler, Johannes Prajapat, Manish As, Yarden Zeilinger, Melanie Fürnstahl, Philipp Krause, Andreas Systems and Control Optimization and Control 93E20 We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can provide guarantees for a large class of distributions, including time-varying distributions. Specifically, we first provide a new characterization of sub-Gaussian random vectors using matrix variance proxy, which can more accurately represent the predicted state distribution. We then derive tail bounds under linear propagation for the new characterization, enabling tractable computation of probabilistic reachable sets of linear systems. Lastly, we utilize these probabilistic reachable sets to formulate a stochastic MPC scheme that provides closed-loop guarantees for general sub-Gaussian noise. We further demonstrate our approach in simulations, including a challenging task of surgical planning from image observations. |
| title | Stochastic Model Predictive Control for Sub-Gaussian Noise |
| topic | Systems and Control Optimization and Control 93E20 |
| url | https://arxiv.org/abs/2503.08795 |