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

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.