{"ID":2863194,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24157","arxiv_id":"2509.24157","title":"Learning Hybrid Dynamics via Convex Optimizations","abstract":"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.","short_abstract":"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 jo...","url_abs":"https://arxiv.org/abs/2509.24157","url_pdf":"https://arxiv.org/pdf/2509.24157v1","authors":"[\"Kaito Iwasaki\",\"Sangli Teng\",\"Anthony Bloch\",\"Maani Ghaffari\"]","published":"2025-09-29T01:15:06Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}