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Model selection for hybrid dynamical systems via sparse regression.

N M Mangan1, T Askham2, S L Brunton3

  • 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA.

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Summary
This summary is machine-generated.

This study introduces Hybrid-Sparse Identification of Nonlinear Dynamics (Hy-SPIN) to analyze complex hybrid systems. Hy-SPIN effectively identifies distinct nonlinear dynamics and switching behaviors from measurement data.

Keywords:
data-driven discoveryhybrid systemsinformation criteriamodel selectionnonlineardynamicssparse regression

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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Information Theory

Background:

  • Classical dynamical systems theory struggles with hybrid systems.
  • Current model identification methods often fail to capture complex, switching behaviors.
  • Hybrid systems are crucial for understanding phenomena in diverse fields.

Purpose of the Study:

  • To develop a novel methodology for identifying nonlinear hybrid systems.
  • To address limitations of existing model identification techniques.
  • To enable robust analysis of systems exhibiting switching dynamics.

Main Methods:

  • Developed Hybrid-Sparse Identification of Nonlinear Dynamics (Hy-SPIN).
  • Utilized nonlinear geometry of measurement data to construct coordinates.
  • Employed clustering in measurement-based coordinates to identify system regimes.
  • Incorporated information theory to manage uncertainty in identification.

Main Results:

  • Successfully identified separate nonlinear dynamical regimes within hybrid systems.
  • Characterized switching behaviors between different dynamic states.
  • Demonstrated efficacy on numerical examples, including a mass-spring hopping model and an infectious disease model.
  • Validated the ability to perform nonlinear system identification without local time constraints.

Conclusions:

  • The Hy-SPIN methodology provides a powerful new tool for nonlinear hybrid system identification.
  • This approach enhances understanding of complex systems with switching dynamics.
  • Applications include disease modeling, robotics, and cybersecurity.