TR2016-056

Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers' Equation

    •  Benosman, M., Boufounos, P.T., Grover, P., Kramer, B., "Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers' Equation", American Control Conference (ACC), DOI: 10.1109/​ACC.2016.7525157, July 2016, pp. 1673-1678.
      BibTeX TR2016-056 PDF
      • @inproceedings{Benosman2016jul2,
      • author = {Benosman, Mouhacine and Boufounos, Petros T. and Grover, Piyush and Kramer, Boris},
      • title = {Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers' Equation},
      • booktitle = {American Control Conference (ACC)},
      • year = 2016,
      • pages = {1673--1678},
      • month = jul,
      • doi = {10.1109/ACC.2016.7525157},
      • url = {https://www.merl.com/publications/TR2016-056}
      • }
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  • Research Areas:

    Control, Dynamical Systems

Abstract:

We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a modelfree extremum seeking (ES) dither-based algorithm to optimally learn the closure models' parameters. We first propose to auto-tune linear closure models using ES, and then extend the results to a closure model combining linear and nonlinear terms, for better stabilization performance. The coupled Burgers' equation is employed as a test-bed for the proposed tuning method.

 

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