Abstract: A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations,known as the error-in-variables (EIV) problem.Using the orthogonal projection approach to eliminate the noise influence,consistent estimation is guaranteed for the deterministic part of such a system.A strict proof is given for analyzing the rank condition for such orthogonal projection,in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model.In the result,the plant state matrices can be retrieved in a transparent manner from the above matrices.An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.

Key words: closed-loop error-in-variables system, subspace identification, extended observability matrix, orthogonal projection

摘要： A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations,known as the error-in-variables (EIV) problem.Using the orthogonal projection approach to eliminate the noise influence,consistent estimation is guaranteed for the deterministic part of such a system.A strict proof is given for analyzing the rank condition for such orthogonal projection,in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model.In the result,the plant state matrices can be retrieved in a transparent manner from the above matrices.An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.

关键词: closed-loop error-in-variables system, subspace identification, extended observability matrix, orthogonal projection