Subspace identification algorithms are established for stochastic, deterministic and combined stochastic-deterministic identification. In this identificatoin method, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. It is well known that for an infinite amount of data and a correct choice of the system order, this least squares estimate of the system matrices is unbiased. However, for a finite amount of data, the estimated system matrix can become unstable, for a given deterministic system which is known to be stable. In this paper, stability is obtained by adding a regularization term to the least squares cost function. The regularization term used here is the trace of the product of dynamical system matrix, a positive (semi-)definite weighting matrix and the transpose of the dynamical system matrix. The amount of regularization needed can be determined by solving a generalized eigenvalue problem. It is shown that the so-called data augmentation method proposed by Chui and Maciejowski corresponds to adding regularization terms with specific choices for the weighting matrix.
Co-ordinator(s): Bart
De Moor, Johan
Suykens
Researcher(s): Tony
Van Gestel