Max-Entropy Moment Filtering for Stochastic Hybrid Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910239105744896 |
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| author | Iwasaki, Kaito C., Tejaswi K. Bloch, Anthony Ghaffari, Maani Lee, Taeyoung |
| author_facet | Iwasaki, Kaito C., Tejaswi K. Bloch, Anthony Ghaffari, Maani Lee, Taeyoung |
| contents | Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced probability flux across guard sets, making direct density propagation through hybrid Fokker-Planck equations expensive. We develop a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF) that performs filtering from partial statistical information by propagating a finite collection of moments through stochastic hybrid dynamics and reconstructing beliefs using moment-constrained maximum-entropy distributions. The key step is a moment propagation rule derived from Dynkin's formula with a jump-sum, in which reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. In a stochastic bouncing-ball example, the proposed method captures reset-induced non-Gaussianity through corrected moment equations while retaining the MEM-KF's optimization-based maximum-entropy representation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20411 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Max-Entropy Moment Filtering for Stochastic Hybrid Systems Iwasaki, Kaito C., Tejaswi K. Bloch, Anthony Ghaffari, Maani Lee, Taeyoung Systems and Control 93E11, 93E03, 60H30, 60J25, 35Q84 Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced probability flux across guard sets, making direct density propagation through hybrid Fokker-Planck equations expensive. We develop a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF) that performs filtering from partial statistical information by propagating a finite collection of moments through stochastic hybrid dynamics and reconstructing beliefs using moment-constrained maximum-entropy distributions. The key step is a moment propagation rule derived from Dynkin's formula with a jump-sum, in which reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. In a stochastic bouncing-ball example, the proposed method captures reset-induced non-Gaussianity through corrected moment equations while retaining the MEM-KF's optimization-based maximum-entropy representation. |
| title | Max-Entropy Moment Filtering for Stochastic Hybrid Systems |
| topic | Systems and Control 93E11, 93E03, 60H30, 60J25, 35Q84 |
| url | https://arxiv.org/abs/2605.20411 |