TR2017-062

Robust POD Model Stabilization for the 3D Boussinesq Equations Based on Lyapunov Theory and Extremum Seeking


    •  Benosman, M., Borggaard, J., Kramer, B., "Robust POD Model Stabilization for the 3D Boussinesq Equations Based on Lyapunov Theory and Extremum Seeking", American Control Conference (ACC), DOI: 10.23919/ACC.2017.7963218, May 2017.
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      • @inproceedings{Benosman2017may,
      • author = {Benosman, Mouhacine and Borggaard, Jeff and Kramer, Boris},
      • title = {Robust POD Model Stabilization for the 3D Boussinesq Equations Based on Lyapunov Theory and Extremum Seeking},
      • booktitle = {American Control Conference (ACC)},
      • year = 2017,
      • month = may,
      • doi = {10.23919/ACC.2017.7963218},
      • url = {https://www.merl.com/publications/TR2017-062}
      • }
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  • Research Area:

    Dynamical Systems


We present new results on robust model reduction for partial differential equations. Our contribution is threefold: 1.) The stabilization is achieved via closure models for reduced order models (ROMs), where we use Lyapunov robust control theory to design a new stabilizing closure model that is robust with respect to parametric uncertainties; 2.) The free parameters in the proposed ROM stabilization method are autotuned using a data-driven multi-parametric extremum seeking (MES) optimization algorithm; and 3.) The challenging 3D Boussinesq equation numerical test-bed is used to demonstrate the advantages of the proposed method.