ECE Seminar - System Identification without Identifying System Roots 

Abstract: System identification has long been a topic of interest in control community, and many classic algorithms are successively derived and proved to be asymptotically unbiased, such as the Ho-Kalman algorithm and the subspace methods. However, when only finite samples are available, the ill-conditionedness of certain algorithms are observed both in theory and in practice. In this talk, we first provide an analysis on the ill-conditioned problem, and prove that both the Ho-Kalman algorithm and the identification problem itself are ill-conditioned. Specifically, the result also shows that the system poles are hard to identify. Motivated by this observation, we then introduce a new identification algorithm by constructing another system with predefined system poles to approximate the input-output relationship of the true system. Both theoretical analysis and numerical results demonstrate the efficiency of the proposed algorithm. Furthermore, we reveal that the proposed algorithm is based on the column similarity of the Vandermonde matrix, which is proved to be ill-conditioned. On the other hand, another algorithm based on the row similarity of the Vandermonde matrix is briefly introduced.