Learning Hybrid Dynamics via Convex Optimizations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916975080374272 |
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| author | Iwasaki, Kaito Teng, Sangli Bloch, Anthony Ghaffari, Maani |
| author_facet | Iwasaki, Kaito Teng, Sangli Bloch, Anthony Ghaffari, Maani |
| contents | This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear systems (SLSs) and switching polynomial systems (SPSs). We first formulate the joint estimation of the mode dynamics and switching rules as a mixed integer program. To solve its inherent scalability issue, we develop a hierarchy of convex relaxations and establish a bound and conditions under which these relaxations are tight. Building on these results, we propose a bilevel convex optimization framework that alternates between mode assignment and dynamics estimation, and we recover switching boundaries using margin-based polynomial classifiers. Numerical experiments on both linear and nonlinear oscillators demonstrate that the method accurately identifies mode dynamics and reconstructs switching surfaces from trajectory data. Our results provide a tractable optimization-based framework for switching system identification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Hybrid Dynamics via Convex Optimizations Iwasaki, Kaito Teng, Sangli Bloch, Anthony Ghaffari, Maani Optimization and Control Systems and Control 93B30 (Primary), 93C30, 90C25 This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear systems (SLSs) and switching polynomial systems (SPSs). We first formulate the joint estimation of the mode dynamics and switching rules as a mixed integer program. To solve its inherent scalability issue, we develop a hierarchy of convex relaxations and establish a bound and conditions under which these relaxations are tight. Building on these results, we propose a bilevel convex optimization framework that alternates between mode assignment and dynamics estimation, and we recover switching boundaries using margin-based polynomial classifiers. Numerical experiments on both linear and nonlinear oscillators demonstrate that the method accurately identifies mode dynamics and reconstructs switching surfaces from trajectory data. Our results provide a tractable optimization-based framework for switching system identification. |
| title | Learning Hybrid Dynamics via Convex Optimizations |
| topic | Optimization and Control Systems and Control 93B30 (Primary), 93C30, 90C25 |
| url | https://arxiv.org/abs/2509.24157 |