Randomized Subspace Identification for LTI Systems

In this article, a randomized subspace identification (RandSID) method for estimating combined deterministic-stochastic LTI state-space models corresponding to large input-output data is proposed. The main computational burden in conventional subspace methods is due to QR factorization and Singular Value Decomposition (SVD) of various matrices composed of recordings of system inputs and outputs. In the proposed method, these data matrices are first compressed by multiplying with an appropriately sized random matrix. It is shown that the system parameters can be equivalently identified, with no significant degradation in accuracy, by performing the QR and SVD steps on these compressed (smaller) matrices instead of the original ones. Due to this data compression step, the proposed algorithm is significantly faster as compared to conventional methods. The advantages of this method, in terms of computation complexity, are theoretically computed and also demonstrated numerically via various case studies.