Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911317809430528 |
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| author | Liu, Zishun Ma, Liqian Chen, Yongxin |
| author_facet | Liu, Zishun Ma, Liqian Chen, Yongxin |
| contents | We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the probabilistic safety constraint into a tractable deterministic safety constraint on a smaller safe set over deterministic dynamics. As a result, our method is compatible with any off-the-shelf deterministic MPC algorithm. The key to the effectiveness of our method is a tight bound on the stochastic fluctuation of a stochastic trajectory around its nominal version. Our method is scalable and can guarantee safety with high probability level (e.g., 99.99%), making it particularly suitable for safety-critical applications involving complex nonlinear dynamics. Rigorous analysis is conducted to establish a theoretical safety guarantee, and numerical experiments are provided to validate the effectiveness of the proposed MPC method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems Liu, Zishun Ma, Liqian Chen, Yongxin Systems and Control We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the probabilistic safety constraint into a tractable deterministic safety constraint on a smaller safe set over deterministic dynamics. As a result, our method is compatible with any off-the-shelf deterministic MPC algorithm. The key to the effectiveness of our method is a tight bound on the stochastic fluctuation of a stochastic trajectory around its nominal version. Our method is scalable and can guarantee safety with high probability level (e.g., 99.99%), making it particularly suitable for safety-critical applications involving complex nonlinear dynamics. Rigorous analysis is conducted to establish a theoretical safety guarantee, and numerical experiments are provided to validate the effectiveness of the proposed MPC method. |
| title | Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.11584 |