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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11196 |
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| _version_ | 1866912031750225920 |
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| author | Cibulka, Vít Korda, Milan Haniš, Tomáš |
| author_facet | Cibulka, Vít Korda, Milan Haniš, Tomáš |
| contents | This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting of the time and state space. Previous works demonstrated that this splitting could significantly enhance approximation accuracy, although the improvement was highly dependent on the ad-hoc selection of split locations. In this work, we eliminate the need for this ad-hoc selection by introducing an optimization-based method that performs the splits through conic differentiation of the underlying semidefinite programming problem. We provide the differentiability conditions for the split ROA problem, prove the absence of a duality gap, and demonstrate the effectiveness of our method through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs Cibulka, Vít Korda, Milan Haniš, Tomáš Optimization and Control Dynamical Systems This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting of the time and state space. Previous works demonstrated that this splitting could significantly enhance approximation accuracy, although the improvement was highly dependent on the ad-hoc selection of split locations. In this work, we eliminate the need for this ad-hoc selection by introducing an optimization-based method that performs the splits through conic differentiation of the underlying semidefinite programming problem. We provide the differentiability conditions for the split ROA problem, prove the absence of a duality gap, and demonstrate the effectiveness of our method through numerical examples. |
| title | Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2409.11196 |