Neural Autoencoder-Based Structure-Preserving Model Order Reduction and
  Control Design for High-Dimensional Physical Systems
Marco Lepri Davide Bacciu Cosimo Della Santina
This work concerns control-oriented and structure-preserving learning of
low-dimensional approximations of high-dimensional physical systems, with a
focus on mechanical systems. We investigate the integration of neural
autoencoders in model order reduction, while at the same time preserving
Hamiltonian or Lagrangian structures. We focus on extensively evaluating the
considered methodology by performing simulation and control experiments on
large mass-spring-damper networks, with hundreds of states. The empirical
findings reveal that compressed latent dynamics with less than 5 degrees of
freedom can accurately reconstruct the original systems' transient and
steady-state behavior with a relative total error of around 4\%, while
simultaneously accurately reconstructing the total energy. Leveraging this
system compression technique, we introduce a model-based controller that
exploits the mathematical structure of the compressed model to regulate the
configuration of heavily underactuated mechanical systems.