Data-Driven Modeling of Global Bifurcations and Chaos in a Mechanical System under Delayed and Quantized Control

We illustrate how the recent theory of Spectral Submanifolds (SSM) can capture global bifurcations and complex dynamics in mechanical systems even under delay and spatial discretization. Specifically, we build a parameter-dependent SSM-reduced model that predicts global heteroclinic and local bifurcations in a Furuta pendulum under control with delay, and verify these predictions numerically. Under additional spatial discretization of the digital controller, we also obtain an SSM-reduced model that correctly reproduces a numerically and experimentally observed microchaotic attractor in the system.