Optimal input design for system identification in the presence of undermodeling

An optimal input design problem for linear system identification is studied in the presence of undermodeling. To obtain a reduced-order model which approximates the true system in frequency weighted L₂-norm through an open-loop experiment, an indirect identification method is adopted: first, a full-order model is identified via a prediction error method (PEM); Second, the obtained full-order model is reduced to the model of assigned structure via L₂-model reduction. Then, the input spectrum can be optimized for the reduced-model identification instead of the true model by solving a linear matrix inequalities (LMIs) optimization problem. A numerical example demonstrates how the proposed method works. The result implies that the input signal should be optimized for the reduced order system not for the true system to achieve better estimation accuracy.