Model selection for hybrid dynamical systems via sparse regression

TL;DR

This paper introduces Hybrid-SINDy, a novel method for identifying and characterizing hybrid dynamical systems with switching behaviors using sparse regression and data clustering, demonstrated on numerical examples.

Contribution

The paper develops Hybrid-SINDy, a new approach that identifies separate regimes and switching behavior in hybrid systems from measurement data.

Findings

Successfully applied to a mass-spring hopping model

Effectively characterized an infectious disease model

Demonstrated broad applicability to complex systems

Abstract

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics (Hybrid-SINDy), which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty, and characterizes switching behavior. Specifically, we utilize the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass-spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviors is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots, and the protection of cyber infrastructures.