We are presenting the following paper at the 61st IEEE Conference on Decision and Control December 6-9, 2022, in Cancún, Mexico:
Using Spectral Submanifolds for Nonlinear Periodic Control
Florian Mahlknecht, John Irvin Alora, Shobhit Jain, Edward Schmerling, Riccardo Bonalli, George Haller, Marco Pavone
https://arxiv.org/abs/2209.06573
This is the first publication of a broader research project on reducing high-order models using Spectral Submanifolds and exploiting the resulting reduced order models for control. This is a joint effort by Prof. Georg’s Hallers group on Nonlinear Dynamics at ETH Zurich and the Autonomous Systems Laboratory at Stanford University led by Prof. Marco Pavone. The follow-up work uses a data-driven method to obtain a representation of the manifold and successfully demonstrates its applicability to control a soft robot:
Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots
John Irvin Alora, Mattia Cenedese, Edward Schmerling, George Haller, Marco Pavone
https://arxiv.org/abs/2209.05712