New Development in Subspace System Identification via Realization Theory

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The objective of this research project is to develop new subspace identification methods for multivariable systems based on deterministic and stochastic realization theories. The following are the results of the research for the last three years.1. The role of LQ decomposition in subspace methods is clarified by showing that each column of L-matrix is a pair of input-output vectors generated by given input-output data [R6, R8].2. Subspace identification algorithms of identifying closed-loop systems are derived using the ORT (orthogonal decomposition based subspace identification) method by using joint input-output approach [J1] and by the two-stage method [J5, R1]. Moreover, the two stage method is applied to the identification of industrial process [R5].3. Anew stochastic realization algorithm is derived by using LQ decomposition in Hilbert space [J3], and it is successfully applied to the closed-loop stochastic realization [R7]. Also, a finite-interval stochastic balanced realization is analyzed and it is shown that the finite-interval balanced realization algorithm provides stable minimum-phase models under the assumption that an exact finite covariance sequence is available [J4, R2].4. Identification methods for error-in-variables models are developed by using J-spectral factorization And H-infinity identification technique [R4, R9]. Moreover, new identification algorithms are derived by combining the EM algorithm and ORT method in order to cope with outliers in observed data [J2, R3].5. An English monograph for subspace methods for system identification is published from Springer-Verlag, which is suitable for a textbook of graduate students and of applied scientists [B1].