Subspace-based methods for the identification of linear time-invariant systems
This tutorial paper explains various subspace-based methods for the identification of linear time-invariant systems. Realization based methods compute the singular value decomposition of the Hankel matrix of the system and the observability and controllability matrices are obtained from this decomposition. They lead, following the known method of Ho and Kalman, to the system matrices. The idea of the direct method consists in projecting the column vectors of a matrix of output data on a space whose range coincides with the range of the observability matrix of a realization of the system. The observability matrix is taken as the matrix left singular vectors of the projected quantity. The system matrices defining the observability matrix are deduced. The other system matrices appear linearly in the overdetermined input-output equation and can be obtained from this equation. When there is noise in the input-output equation, the author shows how instrumental variable methods allow to eliminate their effect in the procedure. In this context, \(Q- R\) methods allow to obtain a complete stochastic realization but the details are not given. A simulation shows that these methods perform comparably to the prediction error method when the input is white but not as well when the input is not rich enough. In formula (25), the presence of noise is not justified since the corresponding section handles the deterministic case.
scientific article; zbMATH DE number 867791
scientific article