19 December 2023
Several domains such as continuum mechanics, fluid dynamics, quantum systems, and financial markets exhibit high-dimensional dynamics. A useful approach for effective control of such systems is to find low-dimensional approximations that preserve their key structural properties.
In machine learning, a wealth of research focuses on approximating complex nonlinear dynamical systems while ensuring the learned dynamics fulfil specific structural properties, which enabled application to model-based control. The case of direct learning of a compressed dynamics of a high-dimensional system has also been thoroughly investigated in the literature and applied to model-based control.
In this work, EMERGE partners from Delft University of Technology and University of Pisa go a step further in that direction by combining deep learning with structure-preserving model order reduction with a focus on mechanical systems.
The authors investigate the integration of neural autoencoders in model order reduction, while at the same time preserving Hamiltonian or Lagrangian structures. They 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 behaviour with a relative total error of around 4%, while simultaneously accurately reconstructing the total energy. Leveraging this system compression technique, they introduce a model-based controller that exploits the mathematical structure of the compressed model to regulate the configuration of heavily underactuated mechanical systems.
Source: M. Lepri, D. Bacciu and C. D. Santina, "Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systems," in IEEE Control Systems Letters, vol. 8, pp. 133-138, 2024, doi: 10.1109/LCSYS.2023.3344286.
Access EMERGE publications in the link below.
More Information
