TR2021-059

Robust Adaptive Dynamic Mode Decomposition for Reduce Order Modelling of Partial Differential Equations


    •  Kalur, A., Nabi, S., Benosman, M., "Robust Adaptive Dynamic Mode Decomposition for Reduce Order Modelling of Partial Differential Equations", American Control Conference (ACC), May 2021.
      BibTeX TR2021-059 PDF
      • @inproceedings{Kalur2021may,
      • author = {Kalur, Aniketh and Nabi, Saleh and Benosman, Mouhacine},
      • title = {Robust Adaptive Dynamic Mode Decomposition for Reduce Order Modelling of Partial Differential Equations},
      • booktitle = {American Control Conference (ACC)},
      • year = 2021,
      • month = may,
      • url = {https://www.merl.com/publications/TR2021-059}
      • }
  • MERL Contacts:
  • Research Areas:

    Control, Dynamical Systems

Abstract:

This work focuses on the design of stable reduced-order models (ROMs) for partial differential equations (PDEs) with parametric uncertainties. More specifically, we focus here on using dynamic mode decomposition (DMD) to reduce a PDE to a DMD-ROM and then pose the ROM stabilization or closure problem in the framework of nonlinear robust control. Using this robust control framework, we design two DMD-ROM closure models that are robust to parametric uncertainties and truncation of modes. We finally add an adaptation layer to our framework, where we tune the closure models in real-time, using data-driven extremum seeking controllers.