Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.
@article{arxiv.2209.06573,
title = {Using Spectral Submanifolds for Nonlinear Periodic Control},
author = {Florian Mahlknecht and John Irvin Alora and Shobhit Jain and Edward Schmerling and Riccardo Bonalli and George Haller and Marco Pavone},
journal= {arXiv preprint arXiv:2209.06573},
year = {2022}
}
Comments
8 pages, 6 figures, conference on decision and control 2022