A Time Splitting Based Optimization Method for Nonlinear MHE
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913998944862208 |
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| author | Wu, Shuting Wang, Yifei Wang, Jingzhe Rikos, Apostolos I. Du, Xu |
| author_facet | Wu, Shuting Wang, Yifei Wang, Jingzhe Rikos, Apostolos I. Du, Xu |
| contents | Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the \textit{curse of dimensionality} arising from increasing problem complexity and growing length of time horizon. To address this issue, we propose novel computationally efficient algorithms for solving nonlinear MHE problems. Specifically, we first introduce a distributed reformulation utilizing a time-splitting technique. Leveraging this reformulation, we develop the Efficient Gauss-Newton Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) to achieve computational efficiency. Additionally, to accommodate limited computational capabilities inherent in some sub-problem solvers, we propose the Efficient Sensitivity Assisted ALADIN, which enables sub-problems to be solved inexactly without hindering computational efficiency. Furthermore, recognizing scenarios where sub-problem solvers possess no computational power, we propose a Distributed Sequential Quadratic Programming (SQP) that relies solely on first- and second-order information of local objective functions. We demonstrate the performance and advantages of our proposed methods through numerical experiments on differential drive robots case, a practical nonlinear MHE problem. Our results demonstrate that the three proposed algorithms achieve computational efficiency while preserving high accuracy, thereby satisfying the real-time requirements of MHE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Time Splitting Based Optimization Method for Nonlinear MHE Wu, Shuting Wang, Yifei Wang, Jingzhe Rikos, Apostolos I. Du, Xu Systems and Control Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the \textit{curse of dimensionality} arising from increasing problem complexity and growing length of time horizon. To address this issue, we propose novel computationally efficient algorithms for solving nonlinear MHE problems. Specifically, we first introduce a distributed reformulation utilizing a time-splitting technique. Leveraging this reformulation, we develop the Efficient Gauss-Newton Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) to achieve computational efficiency. Additionally, to accommodate limited computational capabilities inherent in some sub-problem solvers, we propose the Efficient Sensitivity Assisted ALADIN, which enables sub-problems to be solved inexactly without hindering computational efficiency. Furthermore, recognizing scenarios where sub-problem solvers possess no computational power, we propose a Distributed Sequential Quadratic Programming (SQP) that relies solely on first- and second-order information of local objective functions. We demonstrate the performance and advantages of our proposed methods through numerical experiments on differential drive robots case, a practical nonlinear MHE problem. Our results demonstrate that the three proposed algorithms achieve computational efficiency while preserving high accuracy, thereby satisfying the real-time requirements of MHE. |
| title | A Time Splitting Based Optimization Method for Nonlinear MHE |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2503.23324 |