  We present a low-order modeling technique for actuated flows based on the
regularization of an inverse problem. The inverse problem aims at minimizing
the error between the model predictions and some reference simulations. The
parameters to be identified are a subset of the coefficients of a polynomial
expansion which models the temporal dynamics of a small number of global modes.
These global modes are found by Proper Orthogonal Decomposition, which is a
method to compute the most representative elements of an existing simulation
database in terms of energy. It is shown that low-order control models based on
a simple Galerkin projection and usual calibration techniques are not viable.
They are either ill-posed or they give a poor approximation of the solution as
soon as they are used to predict cases not belonging to the original solution
database. In contrast, numerical evidence shows that the method we propose is
robust with respect to variations of the control laws applied, thus allowing
the actual use of such models for control.
