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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2410.09857 |
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| _version_ | 1866910648411095040 |
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| author | Li, Yudong Cong, Yirui Zhou, Xiangyun Dong, Jiuxiang |
| author_facet | Li, Yudong Cong, Yirui Zhou, Xiangyun Dong, Jiuxiang |
| contents | This article studies the Set-Membership Smoothing (SMSing) problem for non-stochastic Hidden Markov Models. By adopting the mathematical concept of uncertain variables, an optimal SMSing framework is established for the first time. This optimal framework reveals the principles of SMSing and the relationship between set-membership filtering and smoothing. Based on the design principles, we put forward two SMSing algorithms: one for linear systems with zonotopic constrained uncertainties, where the solution is given in a closed form, and the other for a class of nonlinear systems. Numerical simulations corroborate the effectiveness of our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Set-Membership Smoothing Li, Yudong Cong, Yirui Zhou, Xiangyun Dong, Jiuxiang Systems and Control This article studies the Set-Membership Smoothing (SMSing) problem for non-stochastic Hidden Markov Models. By adopting the mathematical concept of uncertain variables, an optimal SMSing framework is established for the first time. This optimal framework reveals the principles of SMSing and the relationship between set-membership filtering and smoothing. Based on the design principles, we put forward two SMSing algorithms: one for linear systems with zonotopic constrained uncertainties, where the solution is given in a closed form, and the other for a class of nonlinear systems. Numerical simulations corroborate the effectiveness of our theoretical results. |
| title | Optimal Set-Membership Smoothing |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.09857 |