Learning Hybrid Dynamics via Convex Optimizations

Fuente: arXiv
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Main Authors: Iwasaki, Kaito, Teng, Sangli, Bloch, Anthony, Ghaffari, Maani
Format: Preprint
Published: 2025
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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
id 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