Topological Dynamics via Learned Hybrid Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918197135933440 |
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| author | Rivas, Bernardo Iwasaki, Kaito Kalies, William Bloch, Anthony Ghaffari, Maani |
| author_facet | Rivas, Bernardo Iwasaki, Kaito Kalies, William Bloch, Anthony Ghaffari, Maani |
| contents | The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory have provided a rigorous framework for this analysis. However, the computation relies on rigorous outer approximations of the dynamics over a discretized state space, which is challenging to obtain from scattered trajectory data. We propose a methodology that integrates recent advances in switching system identification via convex optimization to bridge this gap between data and topological analysis. We leverage the identified switching system to construct combinatorial outer approximations. This paper outlines the integration of these methods and evaluates the efficacy of computing Morse graphs versus data-driven and statistical approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Dynamics via Learned Hybrid Systems Rivas, Bernardo Iwasaki, Kaito Kalies, William Bloch, Anthony Ghaffari, Maani Dynamical Systems Optimization and Control 37B30 (Primary) 93B30, 93C30, 90C25 (Secondary) The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory have provided a rigorous framework for this analysis. However, the computation relies on rigorous outer approximations of the dynamics over a discretized state space, which is challenging to obtain from scattered trajectory data. We propose a methodology that integrates recent advances in switching system identification via convex optimization to bridge this gap between data and topological analysis. We leverage the identified switching system to construct combinatorial outer approximations. This paper outlines the integration of these methods and evaluates the efficacy of computing Morse graphs versus data-driven and statistical approaches. |
| title | Topological Dynamics via Learned Hybrid Systems |
| topic | Dynamical Systems Optimization and Control 37B30 (Primary) 93B30, 93C30, 90C25 (Secondary) |
| url | https://arxiv.org/abs/2511.08737 |