Model selection for hybrid dynamical systems via sparse regression

August 10, 2018

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.

Introduction

The high-fidelity characterization of complex systems is of paramount importance to manage modern infrastructure and improve lives around the world. However, when a system exhibits nonlinear behavior and switches between dynamical regimes, as is the case for many large-scale engineered and human systems, model identification is a significant challenge. These hybrid systems are found in a diverse set of applications including epidemiology [1], legged locomotion [2], cascading failures on the electrical grid [3], and security for cyber infrastructure.

Fig 3.2

Steps for local validation and selection of models. For each cluster from the training set, we identify validation time-series points that are local to the training cluster centroid (black dots, panel 1). We simulate time-series for each model in the cluster library, starting from each point in the validation cluster (teal, gold and purple dots) and calculate the error from the validation time-series. Using this error we calculate a relative AICc value and rank each model in the cluster (panel 2). We collect the models with significant support into a library, keeping track of their frequency across clusters. The highest frequency models across clusters are shown in panel 3. Note that the colors associated with each model in panel 3 are consistent across panels.