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

TL;DR

This paper demonstrates how Spectral Submanifolds (SSM) theory can effectively model and predict complex bifurcations and chaos in a delayed and discretized mechanical system, validated through numerical and experimental results.

Contribution

It introduces a parameter-dependent SSM-reduced modeling approach for delayed and spatially discretized control systems, capturing global bifurcations and chaos.

Findings

Successfully predicts heteroclinic and bifurcations in a delayed Furuta pendulum.

Reproduces microchaotic attractors observed experimentally.

Validates SSM-based models through numerical and experimental data.

Abstract

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.