Using Spectral Submanifolds for Nonlinear Periodic Control

Conference paper (2022)

Authors

Florian Mahlknecht Stanford University

John Irvin Alora Stanford University

S. Jain Institute of Mechanical Systems

Edward Schmerling Stanford University

Riccardo Bonalli CNRS

George Haller Institute of Mechanical Systems

Marco Pavone Stanford University

Affiliation

External organisation

More Info

expand_more

To reference this document use:

http://resolver.tudelft.nl/uuid:0e316d65-cf55-4329-b523-fe5e7b418f1b

Published Date

2022

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Affiliation

External organisation

Abstract

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.