Data-Driven Bifurcation Analysis via Learning of Homeomorphism

Autor:	Tang, Wentao
Rok vydání:	2023
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism that transforms the underlying system to a reference linear dynamics -- either an explicit reference model with desired qualitative behavior, or Koopman eigenfunctions that are identified from some system data under a reference parameter value. When such a homeomorphism fails to be constructed with low error, bifurcation phenomenon is detected. A case study is performed on a planar numerical example where a pitchfork bifurcation exists. Comment: 12 pages, 4 figures, submitted to the 6th Annual Learning for Dynamics and Control (L4DC) Conference
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.06634 Zobrazit plný text záznamu View this record from Arxiv